CENTERNIST Measurement Services:

/ypp 1 8 1994

NIST Pressure Calibration

Service

NISTSpecial

Publication

250-39

Vern E. Bean

U.S. Department of CommerceTechnology Administration

National Institute of Standards and Technology

NIST MEASUREMENT SERVICES:NIST Pressure Calibration Service

Vern E. Bean

Chemical Science and Technology Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899

February 1994

U.S. Department of CommerceRonald H. Brown, Secretary

Technology Administration

Mary L. Good, Under Secretary for Technology

National Institute of Standards and TechnologyArati Prabhakar, Director

National Institute of Standards and Technology Special Publication 250-39

Natl. Inst. Stand. Technol. Spec. Publ. 250-39, 98 pages (Feb. 1994)

CODEN: NSPUE2

U.S. GOVERNMENT PRINTING OFFICEWASHINGTON: 1994

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325

PREFACE

This document describes the NIST Pressure Calibration Serviceso that others may benefit from the years of experience of the NISTpressure metrologists . It is snapshot of the service on 1 October1992. Since pressure metrology is an active area of research at

NIST, this document will become dated as methods, apparatus and

uncertainties improve.

TABLE OF CONTENTS

page

I. NIST PRESSURE CALIBRATION SERVICE. 1

II. DESIGN PHILOSOPHY AND THEORY. 1

A. Mercury Manometer. 1

B. Controlled-clearance Primary Standard Piston Gages. 4

1. Mass. 7

2. Local acceleration due to gravity. 7

3. Air buoyancy correction. 8

4. Surface tension correction. 9

5. Dimensional metrology of the piston. 11

6. Temperature correction. 13

7. Piston distortion. 14

8. Cylinder distortion. 15

9. Jacket pressure. 19

C. Total Uncertainty of the Primary Standards. 22

D. Transfer Standards and Their Uncertainty. 31

E. Calibration Quality Control. 36

III. CROSS-FLOAT CALIBRATION TECHNIQUE. 42

A. Experimental Arrangement. 43

B. Reference Levels. 47

C. Connections. 49

D. Cleaning. 50

E. Rotation. 51

F. Data Evaluation. 51

IV. INTERNATIONAL INTERCOMPARISONS . 53

A. IMGC. 53

B. BIPM. 58

V. REFERENCES. 63

VI. APPENDIX: SAMPLE CALIBRATION REPORT. 65

V

I. NIST PRESSURE CALIBRATION SERVICE

The National Institute of Standards and Technology (NIST)

provides calibration services for piston gages and pressuretransducers. For gas-operated units, the current pressure range is

7 kPa to 17 MPa (1 to 2500 psi) ; for oil, the range is 1.1 to

280 MPa (160 to 40,000 psi). Special tests for gas-operated unitsmay be performed as low as 1.4 kPa. Routine calibrations of pistongages are done using the cross-floating technique with NISTtransfer standard piston gages. The uncertainties in piston gageeffective areas associated with the NIST transfer standard pistongages are plotted in figures 1 and 2 as a function of pressure for

gas and oil respectively. Both plots represent the use of severaltransfer standards. For gas, the uncertainty ranges between 2 2 to

50 parts per million (ppm) ; for oil, it ranges between 40 and 86

ppm. The uncertainties are based on tripled standard deviationsand are discussed in Sections II. C and II. D.

Shipping instructions and scheduling are available bytelephoning the Pressure Group at (301) 975-4832 for gas-operatedgages or (301) 975-4857 for oil-operated gages. The Group Secretarycan be reached at (301) 975-4840.

II. DESIGN PHILOSOPHY AND THEORY

A primary standard for pressure is an instrument that does notrequire a pressure calibration in order to measure pressure; it is

characterized by measuring the fundamental units of mass, time,

length and temperature. Primary standards are used to calibrateNIST transfer standard piston gages, which are then used to

calibrate customers' gages. The primary standards to which the

NIST transfer standards are traceable are a mercury manometer and

controlled-clearance piston gages.

In this section we consider design and operation of the

primary standards, estimated uncertainties for the NIST primarystandards, characterization of the NIST transfer gages, and the

errors due to the calibration process of the transfer gages.

A. Mercury Manometer

1

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The essential feature of a manometer is a vertical column offluid, suitably contained and supported at the bottom by an appliedpressure. The magnitude of the pressure is the product of thecolumn height, the density of the fluid, and the acceleration dueto gravity plus whatever pressure is applied to the top surface of

the fluid column. Thus the manometer is a differential pressuremeasurement device and is used in the absolute mode when the spaceabove the top surface of the fluid column is evacuated, or in thegage mode when that space is at ambient atmospheric pressure. Thegreatest limitations of accuracy are due to the uncertainties in

the density of the fluid and in the column height measurements. In

general, at atmospheric pressure, a state-of-the-art manometer willhave a lower uncertainty than a state-of-the-art primary standardpiston gage.

The piston gage has two advantages over the manometer:

portability and ease of use. These two properties and thestability of the piston gage make it an excellent transferstandard. In order to meet the demand for reduced uncertainties,we have used the manometer that was developed at the NationalBureau of Standards (now NIST) for gas thermometry [1] as a primarystandard to calibrate two essentially identical piston gages,

designated as PG28 and PG29, that serve as the reference standardsfor the NIST gas pressure calibration service. PG28 then was used

to calibrate several of the transfer standards used routinely in

the calibration service.

A complete description of the gas thermometer manometer and an

evaluation of its uncertainties are found in the literature [1-4].

The manometer operates at pressures up to 0.13 MPa in the absolutemode with an uncertainty of 2 ppm based on tripled standarddeviations.

B. Controlled-Clearance Primary standard Piston Gages

The controlled-clearance piston gage has been described by

Heydemann and Welch [5] from which portions of the present

discussion have been extracted.

Essentially, a piston gage is a piston fitted into a matching

4

cylinder filled with fluid, loaded with known weights, and rotatedwith respect to the cylinder to help attain concentricity of thepiston in the cylinder. The rotation both minimizes the possibilityof and aids in the detection of metal-to-metal contact, whichcauses unwanted frictional forces. The upward force due to thepressure in the system acting on the area of the piston is balancedagainst the downward gravitational force due to the weights. Thepressure is defined as the ratio of the downward force to the area.

As the force can be measured with greater accuracy than thearea, the limitation of the accuracy of the gage is in thedetermination of the area and how it changes with pressure due to

elastic distortion of the piston and cylinder.

One method of reducing the effect of the distortion is to

provide a means of applying an auxiliary pressure (known as the

jacket pressure) to the outer surface of the cylinder^~^tQ^ controlthe width of the annulus between the piston and the cylinder, as in

the controlled-clearance piston gage shown in figure 3.

As the effect on the area due to the elastic distortion of thecylinder is several times that due to the piston, controlling the

distortion of the cylinder can provide a significant reduction of

inaccuracy. Furthermore, the ability to control the clearanceallows one to obtain the best operating conditions for theparticular pressure transmitting fluid used.

The pressure, p, generated by a controlled-clearance pistongage operating at its reference level is given by

Mgil - Pa/Pn,)

[1 + (a^ + ttp) (r - T^)] (1 + bp^) [1 + dip^ - pj)]

where

:

M is the mass of the piston plus the total load applied to the

piston,

g is the local acceleration due to gravity,

Pg is the density of the air,

p^ is the density of the metal from which the weights are made,

Y is the surface tension of the fluid.

5

fp

Figure 3. Schematic representation of a controlled-clearance piston gage where P is the pressure under thepiston, F is the total force applied to the piston, andPj is the jacket pressure.

6

C is the circumference of the piston where it emerges from thefluid,

Aq is the area of the piston at the reference temperature and atatmospheric pressure,

is the linear thermal expansion coefficient for the cylinder,

Op is the linear thermal expansion coefficient for the piston,

T is the temperature of the piston and cylinder at the time of thepressure measurement,b is the pressure coefficient of the piston,

p^ is the nominal pressure,

d is the coefficient of the change of area with jacket pressure,p- is the jacket pressure during operation, and

is the jacket pressure for which the clearance between thepiston and cylinder is extrapolated to go to zero.

As all of the terms in eq (1) must be determined, we shallconsider each in turn.

1. Mass

The values of the masses of all the weights used in the NISTpressure calibration service are traceable to the NIST MassStandards Laboratory. An identifying number stamped into eachweight is used to recall the appropriate mass value and densityfrom computer memory. Mass values must be known for all parts of

the piston gage supported by the pressure including the piston,

weight hanger or yoke, the weights, and may include thrustbearings, rotation mechanisms, etc.

2. Local acceleration due to gravity.

The best value of g for a given laboratory site may be

obtained by having on-site measurements made by the Office of

National Geodetic Survey, with uncertainties on the order of 0.1

ppm or better. The next best value of g can be obtained by an

interpolation from a grid of measurements prepared by the same

organization, with typical uncertainties of a few ppm depending on

geographical location. For further information on both of theseservices, contact National Oceanic and Atmospheric Administration,

7

National Ocean Survey, Office of the National Geodetic Survey,Geodetic Information Center, Washington Science Center, Rockville,MD 20852, [(301) 713-3242].

As a third option, the local acceleration due to gravity, gcan be computed from

9=9^- 0.000308671 + 0.0001118 (72 - h^) (2)

where g^ is the sea level acceleration due to gravity, h is theelevation in meters of the site above sea-level, and h^ is the

elevation in meters of the general terrain for a radius of 70 km.

g^ is calculated from

= 980.6160 (1 - 0.0026373 cos 24) + 0.0000059 cos^ 2(|)) (3)

where 0 is the latitude. The value of g calculated in this mannermay have an uncertainty of between 10 and 100 ppm depending on the

locality. Without going to geographic extremes, g can vary by 0.1%

within the continental United States.

The value of g we used until recently was measured in Room 129

of the Mechanical Engineering Building, NIST, Gaithersburg , and is

9.801018 ± 0.000005 m s"^ [6]. The value of g used since 1983,

measured in Room A46 of the Metrology Building, is 9.801011 ±

0.000002 m s'^.

3. Air buoyancy correction.

The air buoyancy correction is given by l-Pg/Pm quite

large. For example, it is 147.5 ppm at 23 °C, 30 percent relativehumidity, and 100 kPa barometric pressure for a stainless steel

weight of density 8 g/cm^. The density of moist air has beentabulated [7,8]. It can be computed from [9]

0 . 0034836 ( P - 0 . 0037960 C7e^), ,

where P is the barometric pressure in Pa , U is the percent of

8

relative humidity, e^ is the saturation vapor pressure of water, T

is the air temperature in kelvins, Z is the compressibility factorfor moist air. is expressed in kg m^. The appropriate valuesof Gg can be calculated from

-5315.56

= 1 .7526 X 10^^ e ^ (5)

where e is the base of natural logarithms. Values of Z are listedin table 1.

A piston gage is a differential pressure measurement devicemeasuring the difference of the pressures applied to the top andbottom of the piston. When the gage is used with the top of thepiston at ambient atmospheric pressure, the unit is operating in

the gage mode. When the gage is used with the top of the piston in

a vacuum, the unit is operating in the absolute mode. When thepiston gage is used in the gage mode, the values for the densitiesof the metals from which the weights are made and which are used in

the calculation of the air buoyancy correction must be theidentical values used by the mass laboratory when the true massvalues are calculated. For this case, the density values can bearbitrary in the sense that they need not be correct for the metalin question, but they must be identical to the values used by themass laboratory.

The situation is different for the absolute mode. Since in

the absolute mode, the air bouyancy force is reduced to zero by

evacuating the space around the weights, an incorrect mass densityvalue used by the mass laboratory will result in an error in themass value. An error of 1 percent in the metal density yields an

error of 1.5 ppm in the pressure. In this case it may be necessaryto determine the density values of the weights by hydrostaticweighing.

All of the NIST controlled-clearance piston gages operate onlyin the gage mode.

4. Surface tension correction.

9

Table 1. Compressibility factor, Z, for COg-free air

Tctnpe r * t ur« 1 at i v« Hun Percentpasc« 1 % Hq) 0 2S 50 75 too

70OO0 C 7 cJ - - 9997 3 . 99972 . 99971 . 99968 . 99960

75000 562 99972 99970 . 99969 9996*80000 600 0 . 999 70 - 99968 777»-» 5

8S000 637 f, 999^8 - 9996 7 ^^^^ 1

90000 675 1 - 99966 - 9996 5 9996 3 9996 1 9995995000 712. 6 9996^ 7 7 70 7 1 99960 -99957100000 750 1 99962 99961 .99959 99958 99956101 }25 760 0 .99962 . 99960 . 99959 .99957 -99955105000 787 6 99959 99958 99956 9995*1 1 0000 825 1 999S8 7777

/

• 99956 9995* 99952

70000 525 0 999 7^ 9997 3 .99971 .99969 9996675000 562 5 99972 9997

'

. 99969 99967 9996*80000 600. 0 99970 99969 .99967 .99965 9996385000 637. 6 99969 9996 7 99966 -9996* 99961

90000 675 1 9996 7 ^^^^^ . 9996*1 99962 9996095000 7I2 6 9996s 9996'i .99962 99960 -99958

t 00000 750 I .99963 .99962 .99960 - 99958 -99956101 )25 760 0 99963 99961 99960 .99958 99956105000 787 6 9996

1

99960 .99958 .99957 9995*I 1 0000 825 1 999S9 999S8 .99957 99955 9995)

70000 525 . 0 9997S 999 7 3 .99971 99969 9996675000 562. 5 9997 3 999 72 .99970 -99967 -9996*80000 600 0 9997

1

999 70 -99968 99966 9996385000 637 6

. 9$$69 . 99966 9996* 9996190000 675 1 99968 99966 -99965 99962 9996095000 712 6 99966 9996s . 9996

1

99961 999581 00000 750 1 9996*. 9996) 99961 99959 99956101 )25 760 0 9996*. 99962 .99961 99959 99956105000 787 6 99962 . 9996

1

.99959 99957 999551 1 0000 825 1

. 99960 - 99959 .99958 99956 99953

70000 525 0 9997 7 999 99972 99969 9996675000 562 - 999 7*«

- 99972 99970 9996880000 600 0 999 72 . 999 7

'

99969 99966 9996385000 637 h . 99970 - 99969 9996* 999^ t

90000 675 1 99968 - 99967 99965 . 99963 9996095000 7 1 2 6 99967 99965 9996 3 9996

1

99958I 00000 750 1 99965 .9996k 99962 99960 9995 7

101 325 760 0 99965 9996 3 -99961 99959 99956105000 787 6 . 9996 3 . 99962 99960 99958 .999551 1 0000 825 1 7770* 99960 . 99958 .99956 9995*

70000 525 0 - 7 7 7 /

0

QQ<1 7<;77 7 /

7

. 99972 . 99969 . ''9966

75000 562 $ - 9997'* - 999 7

)

9997

1

99968 -9996*80000 600 0 7 7 7 ' 5 777 /

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. 99969 99966 9996385000 637 6 9997

1

99969 99967 99965 9996290000 675 1 99969 - 99968 99966 9996 3 9996095000 71 2 - 99968 - 99966 9996k 99962 99959

1 00000 750 1 . 99966 9996*. . 99962 99960 .99957101 325 760 0 99965 -9996*1 99962 99960 .99957105000 787 6 9996^ 9996

)

99961 .99958 .99956

1 I 0000 825 1 - 99963 . 99961 99959 99957 . 9995*

70000 525 0 . 99977 . 99975 9997 3 ^^^^ 9996575000 562 99975 . 9997) 9997

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9996*80000 600 0 99973 99972 99970 99967 .99963

85000 617 ( 99972 99970 .99962

90000 675 1 - 99970 - 99969 .99966 .9996* -99960

95000 71 ?- 99968 . 99967 99965 99962 999^9

1 00000 ^50 1 99967 99965 .99963 .99961 .99957

101 325 760 0 .99966 99965 -999*3 99960 -99957105000 787 6 . 99965 99964 99962 . 99959 999561 1 0000 825 I - 9996^ . 99962 99960 - 9995 7 . 9995*

70000 J'

J

Q 99977 . 99976 9997 3 99970 9996575000 562 - 99976 - 999 7*» 99971 9996*Rnono 600 0 9997^ . 99972 99970 9996 3

85000 6X70 ) / 9997) . 99971 99968 99965 . 99962

90000 67^. 99971 99969 .9996* 99960

.99969 . V9968 99965 . 99962 999597CA

- 99968 - 7 7 7OO 9996* _ I 99958101 325 760 0 99967 99966 9996) 99961 .99957

105000 787 6 99966 .9996<i .99962 .94960 .99956

1 10000 825 . 1 99965 99963 99961 .99958 .99955

70000 525 .0 99978 -99976 9997) .99970 9996575000 562 .5 99976 .99975 .99972 .99968 9996*

80000 600 .0 .99975 .9997) .99970 .99967 -9996)

85000 637 .6 .99973 .99971 -99969 99966 99961

90000 675 . 1 .99972 .99970 .99967 .9996* 9996095000 712 .6 .99970 99968 99966 .99963 .99959

100000 750 . I .99969 99967 .9996* -99961 .99958

101 J25 760 .0 .99968 99966 .9996* -99961 .999571 05000 787 .6 99967 99965 .9996) 99960 999561 10000 825 . 1 .99966 9996* .99961 .99959 99955

2J.0

2*.0

25.0

Z6.0

10

yC is the force generated by the surface tension of the fluidacting on the piston where it emerges from the fluid. y is thesurface tension of the fluid and C is the circumference of thepiston where it emerges from the fluid. The value of the surfacetension for the oil commonly used in NIST piston gages is 3.05 x

-210 N/m and is assumed to be accurate within 10 percent. This is

a small and perhaps negligible correction for high pressure gages

but it may have to be taken into account for oil-operated gages at

low pressures . For example, at 1 . 1 MPa, the correction for a gage

with a piston diameter of 0.010 m is 11 ppm. This correction does

not apply to gas-operated gages.

5. Dimensional metrology of the piston.

Aq is the average cross-sectional area of the piston at

atmospheric pressure as determined from numerous measurements of

the diameter along the length of the piston. For a primarystandard every effort is made to obtain a straight and roundpiston. Polar plots of the deviation of actual piston diameterfrom a nominal diameter are a useful way to check the roundness o

the piston. Figure 4 is such a plot for the piston in the NISTcontrolled-clearance gage known as PG27 with a nominal diameter of

8 mm. In this case, the deviations from being perfectly round do

not exceed 7.5 nm.

The Dimensional Metrology Group of NIST presently claims an"8

uncertainty (one standard deviation) o^ 3.3 x 10 m in the

determination of the diameter of pistoi\s for primary gagesirrespective of their diameter. Thus, on a part-per-million basis,

a perfectly round and straight piston of large diameter will havea smaller uncertainty in area then a small diameter piston of equal

quality.

The value of used in eq (1) is calculated using the

expression

= ^M^) [1 + 2ap(23 - TJ] (6)

where D is the average piston diameter determined from the

dimensional measurements and T is the temperature in °C at which

11

Figure 4. Talyrond of the piston for PG27.

12

these measurements were made. This expression now defines T^ of eq(1) to be 23 °C. The NIST dimensional laboratory is maintained at20 °C to match the dimensional laboratory temperatures of theEuropean national standards laboratories while the NIST pressurelaboratory is maintained at 2 3 "C to match the normal temperatureof the pressure laboratories in American industry; hence, thetemperature correction.

The appropriate value of D to use in eq (6) is a matter ofjudgment where one must consider the piston roundness,straightness , and the most probable location along its length wherecontrolling the clearance between the piston and cylinder willdefine the gage's working area to be. The uncertainty assigned tothe value of D must take into account all of these considerationsas well as the uncertainties of the dimensional measurementprocess

.

6. Temperature correction.

The temperature correction for the area is given by

Cj. = 1 + (a^ + ttp) (r - r^) (7)

The reference temperature T^ is the temperature at which the pistonarea assumes the value A^. For a tungsten carbide piston inside a

steel cylinder the correction is on the order of 17 ppm per °C.

An operating piston gage generates heat in three ways:

(a) adiabatic heating in the fluid due to a rapid pressure change;(b) heat generated by friction in the fluid as it flows up theannulus; and (c) heat generated by the rotation of the piston.

The temperature gradient along the cylinder length of a

hydraulic piston gage is due only to the heat generated by the flowof the fluid up through the annulus and is a function of pressure,viscosity and location along the engagement length. The onlyreported measurements of the temperature gradient are for a simplegage operating at 2 0 MPa. The maximum temperature differencebetween the fluid under the piston and the fluid at any locationalong the piston engagement length was of the order of 60 mK [10].

Heat generated by piston rotation and that due to adiabatic effects

13

serve only to increase the overall temperature of the system but donot contribute to the temperature gradient.

Temperature measurements of the cylinder of an operating gageas a function of jacket pressure indicate the temperature increasesby several hundredths of a degree when a jacket pressure close tothe upper end of the operating range is chosen. This rise has beenused as an indication for the upper limit of the jacket pressurerange

.

Platinum resistance thermometers, thermocouples, andthermistors have been used to detect the small changes in

temperature in piston gages.

The temperature sensing elements, leads, and read-out shouldbe calibrated as a unit. The optimum location for the sensor wouldbe at the working area of the piston and cylinder but this is

seldom possible. Normally, the operating temperature of pistongages is determined either on the base supporting the cylinder oron the lower end of the cylinder, which is a compromise of themeasurement. The effect of this compromise must be considered ona case-by-case basis because of the wide variety in gage design and

in materials of construction.

Thermal expansivity data for many gage materials are listed in

table 2.

7. Piston distortion.

The piston pressure coefficient, b, is computed from elastictheory using the expression [11]

2) = -ilH-l-ii (8)E

where ju is Poisson's ratio and E is the modulus of elasticity for

the material from which the piston is made. Both values can be

obtained from ultrasonic measurements on the piston material withan uncertainty of less than 1 percent.

14

Pistons are frequently made from cemented tungsten carbide.Data for the elastic constants of this and other materials are

listed in table 2. With the data for tungsten carbide C93, the

piston distortion, bp^^, amounts to 2.3 ppm at 4 MPa and to 117 ppm

at 200 MPa.

The calculation of the uncertainty for each parameter in eq

(1) is discussed in Section C. The value of b is the only

parameter of eq (1) that is determined from theory. Since no

satisfactory way of determining the contribution to the uncertaintydue to the inadequacy of the theory for calculating b is available,

Heydemann and Welch [5] suggested that one might multiply the

uncertainty for this term as determined in Section C by a factor of

three as a conservative measure.

8. Cylinder distortion.

The cylinder distortion correction term is

= 1 + G?(p, - Pj)

The value of d can be measured either of two ways:

1. Vary Pj and make corresponding changes in the load on the

piston such that the generated pressure remains constant.

2 . Measure the changes in the generated pressure corresponding to

the changes in Pj

.

Either method requires monitoring the generated pressure which

can be done with any transducer of sufficient sensitivity and short

term stability. In particular, it can be done with a second piston

gage cross-floated against the controlled-clearance piston gage.

In order to develop an expression to determine d from the first

method, we rearrange eq (1) obtaining

W = pAo [1 + (ap + a^) (T - T^) ] (1 + b^) [1 + dip^ - Pj) ] (10)

where W is the numerator of the right hand side of eq (1)

.

Let us designate the controlled-clearance gage as the standard

15

m rt~i oo rf^

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X X X X X

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00 00

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16

and the other gage as the reference. The two piston gages arebrought into balance with some given load on the reference gage.Then a series of small changes in Pj are made with correspondingchanges in W on the standard such as to keep the two gages in

balance. Experience has shown that during the time required for

these measurements, the temperature change in both gages is of no

consequence. Hence, as we apply eq (10) to the standard, thevariables for the cross-float measurements are W, and Pj . In the

term 1+bp^, bp^ is negligible compared to 1 for the present purposeand we will regard the entire term as invariant. Since d alreadyhas been used in eq (10) , we use A to denote the totaldifferential. The relative change in W for the standard gagebecomes

AwW

dAp.(11)

For the purpose of determining d, we now assume d(p2-Pj) is

negligible compared to 1. Solving for d, we obtain

d = AWWApj

For the second method where the change of the generatedpressure is measured as a function of Pj, an analogous analysisyields

d = - Ap13)

The value of d must be determined for a series of pressures

over the operating range of the gage. The value of d is a function

of the pressurizing fluid used in the gage and must be measured for

each fluid.

Figure 5 is a plot of d as a function of load for PG27 whichwas determined by the cross-floating technique.

Experimental values of d are generally dependent upon the

applied load. In order to have an expression for interpolation, we

17

200 250 300 350 400 450 500 550

Force jnewtonsj

Figure 5. Experimental values of d plotted as a function of load.

18

find it convenient to use an empirical equation of the form

d = D + EW + FW^ (14)

which is fitted to the experimental values of d and W.

9. Jacket pressure.

To determine the jacket pressure for which the clearance c is

reduced to zero we make the assumption that the leak rate past thepiston is proportional to the third power of the clearance or that

(dV/dt)^^^ = const ' c (15)

where V is the volume of oil bypassing the pa^ton in time t.

Equation (15) is the basic law for laminar flow betweeh lnfinitelyextended plane and parallel plates. Instead of observing the leakrate, dV/dt, it is equivalent and more convenient to measure thefall rate of the piston, ds/dt, where s is the vertical position ofthe piston. Now we rewrite eq (15) as

(ds/dt) = const • c = const ip^ ~ Pj^ ^1^)

where we have assumed c is directly proportional to the differencebetween p^, and pj . We can now determine p^ from a measurement of

ds/dt. as a function of Pj.

The piston position of an operating piston gage can beconveniently measured with a non-contact capacitance proximitysensor. One method is to mount an aluminum disk on the top of theweight hanger directly over the piston and then position the sensorover the center of the disk. The output of the sensor is displayedon a 250 mm wide strip chart recorder. While the weight stack is

resting on the bottom stops, we raise the disk with shims of knownthickness and thereby calibrate the sensor-recorder combination.The sensor-recorder combination is adjusted such that the pentravels about 80 percent of its full range as the piston falls from

0.5 mm above its reference level to 0.5 mm below its referencelevel and the pen is at the center of the chart when the piston is

19

at its reference level. A stop watch is used to time the piston'sfall through this central 1 mm. Abnormalities in the recordedtrace are helpful in trouble-shooting.

Linear voltage displacement transducers, laserinterferometers, and dial gages have also been used to make fall

rate measurements.

The gage is valved off from the rest of the pressure system so

as to be leak-tight with the exception of the leakage past thepiston through the clearance. Fall rate measurements are then madeas a function of jacket pressure for each of several differentloads over the operating pressure range. During thesemeasurements, the clearance must be large enough to maintain a

fluid film between piston and cylinder at all times. The cube rootof the fall rate is a linear function of the jacket pressure overpart of the range. The data may deviate from this linearrelationship at very high and very low jacket pressures. Wheneither very high or very low jacket pressures are used thetemperature of the piston and cylinder increases by severalhundredths of a degree. At high values of pj this is due tofriction between piston and cylinder. At low jacket pressures it

is due to viscosity in the oil passing through the clearance at

high speed. Either region should be avoided. Friction betweenpiston and cylinder may cause rapid deterioration of both.

In figure 6, the jacket pressure is plotted as a function ofthe cube root of the fall rate for several loads on PG27. Theindividual fall rate lines are extrapolated to zero fall rate wherethey intersect the vertical axis at corresponding values of p^.

The right hand side of figure 6 shows a plot of the p^ as a

function of load. The extrapolation of this curve to zero loadintersects the vertical axis at p^^. A dashed line in the graphindicates the operating jacket pressures, which are chosen from thelinear portions of the fall rate curves near the upper ends.

An equation of the form

= - Kids/dt)^/^ (17)

is fitted to data from within the linear portions of the curves of

20

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21

Pj as a function of (ds/dt) for each load W yielding a value offor each W. Then to obtain an expression for interpolation, an

expression of the form

Pz = Pzo + S^W + q^W^ (18)

is fitted to the p^CW) data.

Pj and p^ are dependent upon the pressurizing fluid and mustbe measured for each fluid used.

C. Total Uncertainty of the Primary Standards.

As of 1 October 1992, the primary standard supporting the gaspressure calibration service is the NIST gas thermometer manometer(GTM) . The primary standards for the oil pressure calibrationservice are three controlled-clearance piston gages.Identification numbers and pressure ranges are listed in table 3.

The uncertainty for the GTM over its pressure range is 2 ppmbased on tripled standard deviations [1-4]. For the controlled-clearance piston gages, each of the parameters of eq (1)

contributes to the overall uncertainty of the pressure calculationfor these piston gages. The fractional uncertainty in p can becalculated from

^ =

P

where the Xj are the parameters of eq (1).

As the estimated uncertainties for some of the parametersincrease as the pressure increases, it is customary to state the

most pessimistic case, that is, the uncertainty at maximumpressure. Tables 4-6 list the values of the parameters of eq (1)

required to specify the maximum pressure, the expressions andvalues for each of the normalized partial derivatives, the

uncertainties in the measurement of the parameters, and theresulting relative pressure uncertainties for each of thesecontrolled-clearance gages.

^[p dx^\

22

Table 3. NIST Primary Pressure Standards

NIST designation Pressure ranges Media

(MPa)

GTM

PG27

PG20

PG67

0.01 to 0.13

2 to 28

30 to 140

37 to 280

gas

oil

oil

oil

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26

The temperature of the NIST Dimensional Metrology Laboratoryis maintained at 20 "C to match the temperature of the dimensionallaboratories in European national standards laboratories. The NISTPressure Measurement Laboratories are maintained at 2 3 °C to matchthe temperature most commonly found in U.S. industrial metrologylaboratories. The last two entries in tables 4-6 marked (*) arethe uncertainties due to changing the reference temperature from

2 0 °C to 2 3 °C.

The estimates for the uncertainties of each parameter (dx,)

are given as one standard deviation (1 a). These estimates comefrom a number of sources. In the case of M, g, a^, and a., theestimates are provided by the laboratories that made thecorresponding measurements. The uncertainty in is estimated on

the basis of the comparison in other laboratories of measurementswith the calculations we have used. Since the controlled-clearancegages operate only in the gage mode and the identical values of

used by the mass laboratory in determining the true mass valueswere used for the air buoyancy correction, the uncertainty in p^^ is

zero. The measurements of y are assumed to be accurate to within10 percent. As previously mentioned, the uncertainty in is

based on judgment of the departure of the piston from a perfectlyround and straight cylinder and on the quality of the dimensionalmeasurement process. The uncertainty in the value of b is assumedto be within three percent. The uncertainty in T-T^ is based on

the calibration and location of the temperature probes. For p^, and

d, the uncertainties are the standard deviations of the residualsfrom fitting empirical equations to the pertaining data. Thecalibration of the gage on the jacket pressure system gives rise to

the uncertainty in Pj

.

Each of these controlled-clearance standard piston gages has

its own peculiarities that require some comment in addition to the

data given in tables 4-6.

PG27

This gage represents a departure from the earlier design

philosophy in that formerly the pistons and cylinders were usually

custom made by outside contractors to NIST specifications. PG27

27

was designed around a commercially available piston and cylinder.Because of the required roundness and straightness of the pistonand the cylinder bore and because of the small clearance betweenthem, the manufacture of these parts demands great skill developedby long experience. Typically, a firm that produces excellentpistons and cylinders in a given material, geometry, and sizecannot maintain that quality for a custom job wherein any of thesethree factors are changed until they have again developed the skillrequired by the new circumstances through long experience. Thus,

custom designs of the highest quality are now far more expensivethan commercially available designs of equal quality.

The piston and cylinder of PG27 were made of tungsten carbide.The mounting as a controlled-clearance piston gage is an NISTdesign employing as many commercially available parts as possible.Figure 7 is a diagram of PG27.

The values of d and p^ given in table 4 are appropriate for

28 MPa. For any pressure, d can be expressed by the empiricalrelation

diPa"^) = 3.425 X 10"^2 - 2.974 x 10"^^Pv^

where W is in newtons. p^ is given by

p^(Pa) = 4.013 X 10'' + 1.498 X 10^ W

PG2 0

PG20 is an NIST design and is shown in figure 8. In this casethe piston and cylinder are made of tool steel. The unusualfeature of this gage is the nonuniform wall thickness of thecylinder, the outer diameter of which was tailored in an attempt to

obtain smoother and more uniform operation. As a result, d is an

exponential function of W,

28

n-r-1 nrj ^

thrust bearing

housing

pressure port jacket pressure port

Figure 7. PG27 controlled-clearance piston gage.

29

upper stop bearing

Figure 8. PG20 controlled-clearance piston gage.

30

d(Pa-i) = 8.662 X 10-^2 ^^"•'1''

and

p^(Pa) = 9.3 09 X 10^ + 2.620 x 10"^ W - 0.84 01Pv^2

PG67

Like PG27, PG67 has a commercially available tungsten carbidepiston and cylinder mounted as a controlled-clearance piston gageof NIST design. The mounting design incorporates as manycommercially available parts as possible. It is shown in figure 9.

For this gage,

diPa'^) = 3.691 X 10'^2 _ 2.470 x 10""^"

and

p^iPa) = 3. 9 52 xlO^ + 2. 965 x 10^ W

D. Transfer Standards and Their Uncertainty.

NIST controlled-clearance primary standard piston gages areused to calibrate NIST transfer standard piston gages which are

then used to calibrate customers' gages. The NIST transferstandards are all unmodified, commercially available piston gages.

Use of the transfer standards saves wear on the primary standardsand saves time. The primary standards are generally used only for

international intercomparisons , to calibrate the master gages for

piston gage manufacturers, and to calibrate NIST transfer gages.

As of 1 October 1992, there are four transfer standards usedin the gas calibration program and four for oil. Their NISTdesignations, pressure ranges and pressure media are listed in

table 7.

31

CPc

cc •H•Hu

cm o Cm nH -Hto M-t J-i

^ Q)

4-> 0

in

w(d

(d

Cn

co-pyj

•H

0)

oc

(0

<u

uI

T3Q)

rH

o

4->

Coo

O04

0)

•HPL4

32

Table 7. NIST Transfer Standard Piston Gages

NIST designation Pressure ranges Mediu

PG22 7 to 105 kPa gas

PG34 69 to 1370 kPa gas

PG13 0.41 to 4T MPa gas

PG23 0.7 to 17.3 MPa gas

PG42 1.1 to 29 MPa oil

PG6 7.2 to 104 MPa oil

PG41 14 to 139 MPa oil

PG21 13.8 to 276 MPa oil

A transfer standard is calibrated against a primary standardusing the cross-floating technique. To calibrate a piston gage is

to determine its area as a function of pressure, known as theeffective area, through pressure measurements. This is done byconnecting both gages to a common pressure line, floating bothpistons at their respective reference levels, and assuring both arein equilibrium. The process is repeated for several pressures.The effective area of the transfer standard is calculated fromthe known weights on both gages and the known effective area of thestandard. The details of this procedure are considered in the nextsection.

In general the effective area of a transfer standard can beexpressed as

A, = A,{1 ^ b^p^ + b,p^') (20)

where A^ is the area at atmospheric pressure, b^ and bj are thefirst and second order pressure coefficients, respectively, and p^is the nominal pressure. The values of these coefficients and the

total estimated uncertainties for the eight transfer standard gagesare listed in table 8.

The basis for the total estimated uncertainty for the oil

transfer standards is the sum of the estimated uncertainty (3 o)

for the primary standard and the tripled standard deviation of thepredicted values resulting from the least squares fit to thecalibration data for the transfer standard.

The situation is somewhat more complicated for the gas

transfer standards. The calibrations of the gas transfer standardsare traceable to the GTM. The GTM was designed to operate only in

the absolute mode. While the gas transfer standards can operateeither in the gage or the absolute mode, the gas calibrationservice is operated in the gage mode. There is evidence to suggestthat the effective area for a gas piston gage may not be identical

in the two modes [12]. There is also a body of data that suggeststhe effective area of a gas piston gage also depends upon the gas

used [12]. Both of these effects are under investigation. Toestablish the total estimated uncertainty for the gas transferstandards, we again sum the estimated uncertainty (3 o) for the

34

Table 8. Areas, pressure coefficients, and total estimated uncertainties

of NIST pressure transfer standards

Gage Aq, by b. Uncertainty, ppm

PG22 3.357243x10" 0 0 Note 1

PG34 8.397343x10' 0 0 27

PG13 8.389264x10' 0 0 50

PG23 8.390322x10' -1.48x10-'- 0 50

PG42 8.402138x10-' -2.4xl0-'' 0 Note 2

PG6 1.679672x10' -2.8x10-'' 0 77

PG41 1.680278x10' -2.64x10-'' 0 79

PG21 8.402922x10' -2.81x10-'' 0 85

Note 1. From 7 kPa to 34 kPa, 35 ppm.

From 35 kPa to 105 kPa, 22 ppm.

Note 2. From 1.1 MPa to 2 MPa, 86 ppm.

From 2 MPa to 2.3 MPa, 66 ppm.

From 2.3 MPa to 29 MPa, 60 ppm.

Note 3. All uncertainties are based on tripled standard

deviations.

i 35

primary standard and the tripled standard deviation of thepredicted values for the calibration of the transfer standards andthen increased the sums enough to cover the upper limits of themode and species-of-gas effects. We expect these uncertainties to

be reduced as research progresses and we learn how to calculate andpredict these two effects.

The calibration traceability of the transfer standards andvarious intercomparisons are shown by the diagram in figure 10.

PG23 is a gas-operated gage. Both PG27 and PG6 operate with oil.

Intercomparisons between PG23 and PG6 or PG27 were done using a

gas/oil interface device.

E. Calibration Quality Control.

Primary pressure standards are characterized in terms of

fundamental units, namely: mass, length, time, and temperature.Transfer standards are calibrated through pressure measurementsagainst primary standards.

Confidence in the characterization of a primary standard canbe derived through careful error analysis and by intercomparisonwith other primary standards characterized in other laboratories byother people. Such intercomparisons have been done with othernational standards laboratories and are described in Section IV.

International Intercomparisons.

Confidence in the stability over time of a primary standardcan be achieved through periodic recharacterization or by periodiccalibration of transfer standards and tracking the areas of thetransfer standards as a function of time on control charts. If theareas of the transfer standards remain within acceptable limitsover time, we can then assume both the primary and the transfergages are stable. If the areas do not remain within acceptablelimits, then we may need to recharacterize the primary standard in

terms of fundamental units in an effort to identify the problem.

Figures 11-14 are control charts wherein the relative changeof area with respect to the average has been plotted as a functionof the calendar year in which the NIST pressure transfer standardswere calibrated. There are no control charts for PG2 3, PG3 4, PG41,

36

GAS OIL

PRIMARYSTANDARDS

GTM

REFERENCESTANDARDS

PG28 (0 . 5)

TRANSFERSTANDARDS

PG22 (0.1)

PG34 (1.4)

PG13 (4

)

PG23 (17

PRIMARYSTANDARDS

TRANSFERSTANDARDS

PG2 7 (28)

PG2 0 ( 14 0)^^— .PG21 (276)

PG67 (290)

Figure 10. Intercomparisons involving NIST primary and transferstandard piston gages. The numbers in parenthesis are the maximumpressures of the gages expressed in MPa.

37

aa,

c-rH

(U

CPc

u

>•H4-)

(T3

rHQJ

20 —

-20

1970 1980 1990

Year

Figure 11. The relative change in the area with respect to theaverage (3.357205 E-4) for PG22 as a function of calendar year.The current total uncertainty at the maximum pressure isrepresented by the error bar at the right.

38

30 —

a;

c•H

0)

CPc

u

a)

>•H-Pn3

iHQ)

-30

1970 1980 1990

Year

Figure 12. The relative change in the area with respect to theaverage (8.389305 E-6) for PG13 as a function of calendar year.The current total uncertainty is represented by the error bar atthe right.

39

mQ4

to

0)

u«a

c-H

0)

CPc(0

o

a)

>-H+JrO

rH

40

-40

1970 1980 1990

Year

Figure 13. The relative change in the area at the maximum pressurewith respect to the average (1.679203 E-5) for PG6 as a function ofcalendar year. The current total uncertainty is represented by theerror bar at the right.

40

to

0)

u«j

c•H

<u

tpc

o

>-H+J<0

r-i

<D

50

0

-50

1970 1980 1990

Year

Figure 14. The relative change in the area at the maximum pressurewith respect to the average (8.396495 E-5) for PG21 as a functionof calendar year. The current total uncertainty is represented bythe error bar at the right.

41

and PG42 as they are too new to have a recalibration history.

The recalibration schedule for a transfer standard is an openquestion which depends upon use, abuse, age of the gage, and thematerials from which the piston and cylinder are made. It is

generally accepted by the pressure metrology community that pistonsand cylinders made of tungsten carbide are stable and a

recalibration cycle of a few years is appropriate. However, suchis not the case for steel. There is a report of a new steel pistonin a tungsten carbide cylinder that increased in area by 24.6 ppmover a period of 15 months and by an additional 9.6 ppm during thenext 21 months suggesting the area was becoming asymptoticallystable with time [13]. The suggested cause was the relieving overtime of strains induced by the manufacturing process. Clearly,

such a unit would warrant frequent recalibration until one becameconfident of the stability.

III. CROSS-FLOAT CALIBRATION TECHNIQUE

In principle, we can determine the area and the pressurecoefficient of a piston gage from measurements of the internaldiameter of the cylinder, the diameter of the piston and a

computation of the pressure coefficient using elastic distortiontheory. However, the resulting uncertainties are so large that in

practice piston gage calibrations are done by cross-floatingagainst a standard.

For this technique, both piston gages are connected to a

common pressure line along with an appropriate pressure generator.The effective area, A^, of the test gage is

= F/p (21)

where p is the pressure generated at the reference level of the

test instrument by the standard gage and F is the force exerted on

the piston of the test gage which is

42

1 + (ttp + a^) (r - (22)

For simplicity, the temperature correction of the area has beenincluded with the force. The two gages are brought into pressureequilibrium by adjusting F and then is calculated by eq (21) .

Values of Ag are thus determined over the entire operating pressurerange of the test gage. The effective area at atmosphericpressure, A^, and the coefficients b, and can be obtained byfitting

= Aq{1 + b^p + b^p^) - t/p (23)

to the Ag(p) data obtained from the cross-float measurements, t is

a tare that may indicate an error in the data or may be a propertyof the gage.

A. Experimental Arrangement.

It is essential that the pistons be vertical so that the forcedue to the weights is totally supported by the fluid under thepiston and no component of the force is supported by the cylinderwall. Manufacturers usually mount levels on the piston gage base,provide leveling screws, and assure that the piston is normal to

the base. With many designs a level can be temporarily placeddirectly on the top of the cylinder.

The pressure connections for a cross-float are shownschematically in figure 15. The test instrument (A) is connectedto the standard (B) through a short length of tubing. A valve (C)

can interrupt this connection. The differential pressure indicator(D) can be by-passed by valve (E) . Valve (G) connects to the fluidsupply consisting of a screw pump (H) , gage (K) and reservoir (P) .

If a controlled-clearance piston gage serves as the standard, a

separate supply of jacket pressure is required. Valves (C) and (E)

must be constant-volume valves. Markus [14] has developed a

pneumatically operated constant-volume valve that has been used at

pressures up to 420 MPa and gives very satisfactory service. The

differential pressure indicator should have a sensitivity of at

least one part in one million and should be rugged enough to

withstand the full line pressure applied differentially without

43

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4-)

o

I

y)

(/]

ouu

V-i

o

wco

+J

oCD

CCOo

x:-p

o

E

(13

-H73

O-H4-1

(T3

£

s:uw .

w-p

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<u

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t7> (d

-H 0)

COUJ

44

damage

.

Generally, to calibrate a piston gage using cross-floattechniques, the NIST practice is to make ten measurements at sevenpressures ranging from about ten percent of the full range to thefull range, alternating the direction of rotation of the twoinstruments as shown in table 9. A list of weights to be used onboth gages is prepared in advance and if a controlled-clearancegage is used, the appropriate operating jacket pressures are chosenfrom the plot of jacket pressure as a function of the cube root of

fall rate with load as parameter, such as figure 6.

With valves (C) and (E) open and the weight hangers down on

the stops, both gages are loaded and spun. We prefer to spin gagesby hand and allow them to coast to avoid possible vertical forcecomponents resulting from continuous motor drives. Both pistonsare then raised above their operating level by means of the screwpump (H) and left coasting with valve (G) closed until both gageshave reached temperature equilibrium. With valve (C) closed thedifferential pressure indicator is zeroed by opening valve (E) andmaking the necessary electrical/mechanical adjustments to theindicator. Valve (E) is closed and (C) opened, and the weights on

the test gage are adjusted to zero differential pressure. Whenbalance is attained, the applied loads, the jacket pressure, and

the gage temperatures are recorded. Finally valves (E) and (G) areopened and the pressure is lowered to bring the weight hangers down

to the bottom stop before loading up for the next point.

The function of the differential pressure indicator is to

detect when the two gages are in pressure equilibrium. While the

indicator is convenient, it is not essential. Equilibrium can be

determined by making fall rate measurements. For this techniquethe plumbing system is modified by replacing the differentialpressure indicator with a pressure line and removing the bypass

line and valve. The connection between the two gages now is simply

a pressure line with a constant-volume valve so each gage can be

isolated such that the only fluid loss for each gage is that

bypassing its own piston. With this valve open, the gages are

loaded with appropriate weights to bring the gages near to

equilibrium. Then with the valve closed the fall rate of one of

the gages is measured as the piston is falling through the

45

Table 9. Schedule of points taken during a cross-float

calibration of a piston gage.

Point Pressure Direction of rotation

% of full range standard test

1

2

3

4

5

6

7

8

9

10

10

10

40

70

100

100

85

55

55

25

CW

cw

CW

cw

cw

ccw

ccw

ccw

ccw

ccw

cw

ccw

cw

ccw

cw

ccw

cw

ccw

cw

ccw

46

reference level. The weights on the test gage are then adjusteduntil the fall rate is unchanged whether the valve is open or

closed. This is the equilibrium condition.

There are a variety of ways of making the fall ratemeasurements. A convenient method is to use commercially availableproximity indicators specifically designed for the purpose.Another way is to use the capacitance proximity sensor-strip chartrecorder system described above and observe the slope of therecorded trace as the valve is opened when the falling pistonreaches the reference level. If the slope does not change, the two

gages are in equilibrium. A more cumbersome method is to use a

cathetometer and a stop watch. Whatever the choice of fall ratemeasurement apparatus, it must not add any unknown vertical forces

to the pistons.

B. Reference Levels.

For piston gages with straight pistons, the reference level is

normally defined as the lower end of the piston. For pistons with

an irregular shape of the submerged part, an adjustment of the

reference level is made as illustrated in figure 16. In thisexample the piston has a flange at the lower end serving as a stop.

The volume of the shaded part of the flange is

V = ihTz/4) {D^ - c?2) (24)

If the piston were lengthened such that the volume produced by the

additional length was equal to the volume given by eq (24) , the

length of the piston would increase by

L = SDl^d^ iil.) (25)

where P^/Pj^ ratio of the density of the metal in the shaded

area of figure 16 to the density of the metal in the nonshaded

area. The reference level for a piston of this shape would be

defined as being L below the bottom of the piston.

In a piston gage cross-float, or whenever a piston gage is

47

^ D

REFERENCE LEVEL

Figure 6. Adjustment of reference level for irregularly shapedpistons.

48

used to generate a known pressure at the reference level of anotherinstrument, a correction has to be made for the fluid head in theconnecting line. This correction can be expressed as

P = gHiPfj^ (1 + pK) - p^^J (26)

where g is the acceleration due to gravity, H is the verticalseparation between the reference levels, p^^ is the density of thepressurizing fluid, p is the pressure, k is the compressibility of

the fluid, and pg-^ is the density of the air. /? is subtracted from

the pressure generated by the standard instrument at its referencelevel. The level difference, H, is counted positive upwards from

the reference level of the standard instrument. The term 1 + pK

corrects for the change of density of the fluid with pressure. The

term -pg,,,gH is the head correction due to atmospheric air densityand is used only when the piston gage is operated in the gage mode.

C. Connections.

When connections are made in a pressure system, care should be

taken to install the properly rated tubing, fittings, valves, etc.

Plumbing material should be chosen to be fully compatible with the

pressure fluid. Stainless steels are widely used in liquidsystems, whereas copper, plastics, rubber, etc., are commonly found

in low pressure gas systems. When threading and coning highpressure tubing, it is essential that the threads be carefully made

and that cones have the correct angle and proper finish.

All plumbing should be carefully cleaned. If filters are used

in a system, it is necessary to choose a type that will not break

up or expel particles into the pressure fluid.

To obtain the optimum in response time, lines are usually kept

short and internal diameters should be as large as is practicable.

Damping of a system, if necessary, may be achieved through the use

of needle valves, filters or other types of line restrictions.

Proper valve arrangement can make a system highly efficient

and more 1;han one type of valve may be useful. A constant volumevalve, which operates without disturbing the internal pressure of

the system, is a great advantage when used as the isolation valve

49

between two piston gages in a cross-float situation. Dampingvalves may be employed in a piston gage intercomparison set-upwhere short or long-term oscillations have been detected. Responsetime may suffer as a result of using damping valves, but thissituation may be acceptable if the system is made more stable byusing the valves. Nonrotating stem valves offer the advantage of

long valve seat life.

D. Cleaning.

As in most high precision set-ups containing mechanicalcomponents with moving parts, a clean system is necessary. The oil

piston gage will function properly over a longer period of time if

the instrument, lines, and fittings are carefully cleaned. Damagecan result if particles of dirt become lodged between the pistonand cylinder. Oil piston gages should be cleaned with appropriatesolvents whenever a change is made from one oil to another.

Gas piston gages will not function properly when dirty and if

forced to operate under such conditions, damage to the piston andcylinder is likely.

To obtain the highest performance from a gas piston gage, a

good cleaning technique is essential. One method is to use mildsoap and warm water. The piston and cylinder should be scrubbedthoroughly, rinsed with warm water, air blasted to remove the waterdroplets and finally polished with lens tissue. Before assemblingthe piston and cylinder, dry, clean air (or nitrogen) is used toremove lint particles. The important points in a good cleaningtechnique are: (1) remove all foreign material, such as dirt,

grease, and fingerprints, (2) leave no residue, (3) polish,

(4) remove all remaining lint before assembling. It may be

necessary to repeat the cleaning procedure to obtain satisfactoryresults. The only way to judge how clean is "clean enough" is bythe performance of the gage. If the gage is clean, floating, and

rotating (by hand) on the order of 30 revolutions per minute, it

should take a few minutes to coast to a gradual stop. It is alsoimportant that the remaining plumbing be clean.

Where the removal of the cylinder is difficult or undesirable.

50

it must be cleaned in place. Water should be used with extremecare. It is far safer to use a solvent that will evaporate fairly

rapidly.

The piston gage operator should be able to determine from the

behavior of the instrument (spin time, sensitivity, etc.) whether

the instrument is functioning properly. Proper operatingspecifications should be available from the operators manualprovided by the manufacturer.

E. Rotation.

In most piston gages an electric motor is provided to rotateeither the piston or the cylinder to relieve friction and to

maintain a continuous film of gas or oil between piston and

cylinder. Heat given off by some drive motors may increase the

temperature of the piston and cylinder above the nominal roomtemperature over a period of several hours. Under these conditionsit is difficult to measure the temperature of the piston and

cylinder accurately. Shielding the motor or moving it to a

different location may mitigate the problem.

Some commercial units have drive motors which rotate thepiston assembly much faster than is necessary. High speedrotation of a gas gage can increase the danger of damage. Somemanufacturers recommend the application of a thin film of oil to

the piston and cylinder to prevent galling and to reduce excessivefall rates. While this procedure may lead to an acceptable fall

rate, it will increase friction and reduce sensitivity. Somepiston assemblies are rotated by threads attached to a drivemechanism. Unknown vertical forces will be applied to the pistonif these threads are not kept horizontal when the gage is in

operation. Hand rotation of the piston and weight stack is quitesatisfactory since the optimum speed of rotation can be achievedfor each instrument. A rate of 15 to 20 revolutions per minute is

adequate for most gages.

P. Data evaluation.

We determine the effective area and the coefficients of thetest gage by fitting eight equations to the calibration data and

51

then selecting that which is most appropriate. These equations arevariations of eq (23) and are given below.

(27 . 1)

= \ - t/p (27 . 2)

= A,(l + b^p) (27 . 3)

= A^d + b^p) •- t/p (27 . 4)

= Aod + b^p + bjP^) (27 . 5)

= AJl + b^p + b2P^) - t/p (27 . 6)

= A„(l + b^p^) (27 . 7)

= AJl + b^p^) - t/p (27 . 8)

t may be either a tare error in the data that requiresinvestigation or a coefficient necessary to characterize thebehavior of the gage. At low pressures, the terms involving thepressure coefficients b^ and b2 are usually insignificant and eithereqs (27.1) or (27.2) is used to characterize the gage. At highpressures the coefficient b^ and occasionally also b2 becomesignificant and must be included in the function fitted to the

data. In some cases, the coefficient b^ is insignificant whileis significant.

The computer program used for these computations provides, in

addition to the coefficients, the standard deviations of thecoefficients, the residuals, the standard deviations of theresiduals, and the standard deviations of the predicted values. Aplot of the residuals as a function of pressure will show whetherany gross errors have been made in recording and entering the dataand is a valuable aid in judging which equation is appropriate.One may also separate the data according to the direction of

rotation of either gage and check for effects depending on the

direction of the rotation.

Selecting the proper fit is a matter of judgment based on the

52

residuals, the standard deviations of the residuals, the standarddeviations of the coefficients, and the standard deviations of thepredicted values of the coefficients. The technique is to find thefit having no evident systematic structure in the plot of theresiduals as a function of pressure, having the minimum standarddeviation of the residuals, having the minimum standard deviationof the predicted values of the coefficients, and having no

coefficient that is smaller than its corresponding tripled standarddeviation. When these conditions do not exist for the same fit,

then it is a matter of judgement and compromise. If two fits

represent the data equally well, we would choose the simplerequation

.

Our practice is to express the total uncertainty of the

effective area for the test gage as three times the sum of thestandard deviation of the predicted values for the chosen fit plus

the estimated uncertainty (3 a) of the effective area of thestandard

.

An example of a typical calibration report is in the Appendix.

IV. INTERNATIONAL INTERCOMPARISONS

A primary pressure standard must be characterized in terms of

the fundamental units of mass, length, time and temperature, in

contrast to a secondary standard or transfer standard that is

calibrated through pressure measurements using the primarystandard. An excellent way to test the quality of the

characterization of a primary standard is by comparing it by directpressure measurement with primary standards characterized by otherpersonnel in other laboratories.

Two international intercomparisons of current NIST primarypressure standards have been done which include a bilateralintercomparison of gas gages with Istituto de Metrologia "G.

Colonnetti" (IMGC)[15] and a round-robin intercomparison of oil

gages sponsored by Bureau International des Poids et Mesures

(BIPM) [ 13 , 16]

.

A. IMGC

53

Intercomparisons of pressures generated by a primary standardgas piston gage (IMGC5) of the Istituto di Metrologia "G.

Colonnetti" were made with pressures generated by a transfer gaspiston gage (PG23) of NIST and a primary standard gas piston gage(PG24) of NIST. PG 24 has since been retired.

IMGC5 is a simple piston and cylinder in which the area atatmospheric pressure (determined from the average of the areas of

the piston and of the cylinder) was obtained from directdimensional measurements of the diameters. The pressurecoefficient of the area was determined by IMGC by comparison withanother IMGC simple piston and cylinder gas piston gage of 2 MParange whose pressure coefficient had been calculated theoretically.PG23 has a pressure range of 0.7 to 17.2 MPa and was calibratedagainst the primary standard PG24, but only over the range of 0.7

to 1.9 MPa. PG24 was a primary standard gas-operated,controlled-clearance piston gage with the area derived fromdimensional measurements of the piston only, with an empiricallydetermined correction based on extrapolation of jacket pressurerequired to close the cylinder on the piston, and a theoreticalpressure coefficient applied to the deformation of the piston only.

A total of 21 comparisons at 10 different pressures was madebetween IMGC5 and PG23. Nitrogen was the pressurizing fluid for

all of the measurements. All of the measurements were done in the

gage mode. One method of evaluating the data was to regard PG2 3 as

the standard and IMGC5 as a test gage to be calibrated and applythe usual NIST computer program to determine the areas of IMGC5.

This program determines the effective area and the pressurecoefficient of the test gage in terms of those of the standard.

The lowest order equation, eq (27.1), was selected and gives

an effective area of the IMGC gage of 2.000661x10"^ m^ at 23 °C witha standard deviation of the area of 0.6 ppm. The area of the IMGC

gage given by IMGC is 2.000662x10'^ m^ at 23 °C. The areas are seen

to differ by 0.5 ppm which is less than one standard deviation.

Another method of evaluating the intercomparison was to

calculate the pressure generated by each piston gage according to

the method used by the respective laboratories. The pressures werereferenced to the base of the IMGC piston to account for head

54

corrections. The average of the pressures calculated by IMGC minusthe pressures calculated by NIST is -12.7 Pa with a standarddeviation of the mean of 2 . 0 Pa . The average of the pressurescalculated by IMGC minus the pressures calculated by NIST dividedby the NIST pressure is -5.4 ppm with a standard deviation of themean of 1.0 ppm.

Sixteen comparisons were made between IMGC5 and PG24 at five

different pressures. The same equation (eq (27.1)) was selectedfor this pair of gages. It gives an effective area of the IMGC

-4 2 . . .

gage of 2.000649x10 m at 23 " C with a standard deviation of thearea of 0.6 ppm. The difference in area of the IMGC gage determinedby PG24 in this comparison with that given by IMGC is -6.5 ppm.

The second method of evaluating the intercomparisons was also

applied to this pair of gages. The average of the pressurecalculated by IMGC minus the pressures calculated by NIST is

-6.8 Pa with a standard deviation of the mean of 1 . 1 Pa . Theaverage of the pressures calculated by IMGC minus the pressurescalculated by NIST divided by the NIST pressures is -6.5 ppm witha standard deviation of the mean of 0.6 ppm.

Figure 17 is a plot of the differences in pressure calculatedfrom the characteristics of the gages versus pressure, andfigure 18 is a plot of the relative difference in pressurecalculated from the characteristics of the gages versus pressure.While a systematic difference in pressure is evident in the data,

it is small compared to the estimated systematic uncertainties.

Both methods of expressing the results of the intercomparisonsshow significantly better agreement between the gages (1 to 7 ppm)

than the estimated systematic uncertainty of each of the gages(IMGC5, 24 ppm; PG23, 30 ppm; and PG24, 28 ppm).

The differences observed between IMGC5 and PG24 (the primarystandard), 6.8 ppm by area comparison and 6.5 ppm by pressurecomparison, indicate that the two different methods of calculatingareas are well verified at this pressure range. The differencesobserved between IMGC5 and PG23 (the transfer standard) , 0.5 ppm by

area comparison and 5.4 ppm by pressure comparison, indicate thatthe latter gage serves very well as a transfer standard in the

given pressure range.

55

o

00..cn<Q.

in•-^ o

Z3

Q. o

LU

u- OO 1 0

X-feS-PG24

3 4

PRESSURE. MEGAPASCJkL

Figure 17. Difference in pressure (Pa) versus pressure (MPa) for IMGCS

against PG23 and IMGC5 against PG24. The numbers "2" and "3"

represent the number of replicate data for IMGC5 against PG24

plotted at the same point.

56

o

UJcr

COcnUJdCL

S 2i •

cn

cc

oLU ru

oI 0 3 4

PRESSURE. HEGAPASCAL

IHGC5 YS

Q-NBS-PG23

X-^eS-PG24

Figure 18. Difference in pressure divided by pressure (ppm) versus pressure

(MPa) for IMCG5 against PG23 and IMGC5 against PG24. The numbers

"2" and "3" represent the number of replicate data for IMGC5

against PG24 plotted at the same point.

57

B. BIPM

The Working Group on High Pressure of the Comite Consultatifpour la Masse et les Grandeurs Apparentees of the BureauInternational des Poids et Mesures (BIPM) organized anintercomparison of the primary standard piston gages of 13 nationsin the range of 20 to 100 MPa [13, 16]. The intercomparison wasaccomplished by circulating a transfer standard piston gage amongthe participating laboratories where each calibrated it using theirprimary standard. The data was then sent to the pilot laboratoryfor analysis. This was done in three phases. The participants on

the first phase were Laboratoire National D'Essais (LNE), Paris,

France, which is also the pilot laboratory; Istituto di Metrologia"G. Colonnetti" (IMGC)

,Torino, Italy; Physikalisch-Techniche

Bundesanstalt (PTB),Braunschweig, West Germany; National Physical

Laboratory (NPL),Teddington, United Kingdom; and National Bureau

of Standards (NBS, now National Institute of Standards and

Technology, NIST),Gaithersburg

,MD, USA. The results of the first

phase shown in figure 19 are very instructive. This is a plot of

the relative change of area of the transfer standard as a functionof pressure as determined by each laboratory and compared to a

reference value determined by the pilot laboratory. The curve for

NIST is 14 ppm lower than that published in references. 13 and 16

due to improved thermal expansion data for the piston that was not

available earlier. .

Three features of figure 19 to note are:

1. The maximum spread in the data is 78 ppm which occurs at

the maximum pressure. This is within the combined uncertainties of

the laboratories and is very good agreement.

2. The area of the transfer standard increased by nearly

25 ppm during the year required for these measurements as indicated

by the difference on the curves LNEl and LNE2 obtained before and

after circulation to the other laboratories. The transfer standard

has a steel piston and a tungsten carbide cylinder. If we assume

the total change was in the piston, then the corresponding changein the radius is 60 nm. It has been suggested that the increase in

area is due to relaxation of stresses due to manufacture.

Reference 13 is the first published report of this phenomenon. It

requires further study to be understood. It should not be ignored.

58

50

PPMA

59

3. The slopes of the curves are different which means thatthe various national laboratories do not agree on how the effectivearea of the transfer standard changes with pressure.

The differences in the results from various laboratories arebetter shown by fitting an equation of the form

^ Aq{1 + hp) (28)

to the data from each laboratory and plotting the residuals as a

function of pressure as has been done in figure 20. Three of thecurves, NPL, PTB, and IMGC are concave upward. NPL determined thepressure coefficient of their standard using the "similarity"method [17] wherein two gages of identical geometry, but made of

material having different known elastic moduli are cross-floated,providing data from which the distortion coefficient wascalculated. Both PTB and IMGC calculated the distortioncoefficient using elasticity theory. The three curves LNEl, LNE2

,

and NIST are concave downward. Both of these laboratories usecontrolled-clearance piston gages as their primary standards,

figure 20 implies that there is a fundamental disagreement betweencalculational or similarity methods and the controlled-clearancemethod

.

All of the methods depend upon assumptions that are open to

question. The controlled-clearance technique utilizes an

auxiliary pressure on the outside of the cylinder to control theclearance between the piston and the cylinder. It is assumed thatthe auxiliary pressure is a linear function of the cube root of the

rate at which the piston falls into the cylinder while the gage is

operating for all loads on the piston. It is necessary also to

extrapolate out of the range of these fall-rate measurements to

obtain values used in the cylinder distortion term. The distanceone must extrapolate is greatly influenced by the roundness of thepiston and cylinder. In the derivation of the equation used in thecalculation method, it is assumed that the pressure in the annulusis uniform when, in fact, there is a steep pressure gradient. It

is also assumed that there are no shear stresses between planespassed through the cylinder normal to the cylindrical axis. Thesimilarity method requires the radial separations between the

pistons and cylinders at zero applied pressure be adjusted as

60

Figure 20. Residuals from fitting straight lines to the area data of the

transfer standard provided by each laboratory and plotted as a

function of pressure.

61

closely as possible to be in inverse ratio to the elastic moduli.Then it is assumed that as the pressure is increased, the pressuredistribution between the pistons and cylinders of the two gageswill be the same. Further research is needed to understand and

reconcile the differences.

62

V. REFERENCES

[I] L. A. Guildner, H. F. Stimson, R. E. Edsinger, and R. L.

Anderson, Metrologia 6, 1 (1970).

[2] L. A. Guildner and R. E. Edsinger, J. Res. Natl. Bur. Stand.

(U.S.) 80A, 703 (1976)

.

[3] J. F. Schooley, Proceedings of the 1988 Workshop andSymposium of the National Conference of Standards Laboratories, p.

50-1, August 14-18, 1988.

[4] R. E. Edsinger, and J. F. Schooley, Metrologia 26, 95 (1989) .

[5] P.L.M. Heydemann and B. E. Welch in ExperimentalThermodynamics , Volume II, edited by B. LeNeindre and B. Vodar(Butterworths, London, 1975), pp. 147-201.

[6] D. R. Tate, J. Res. Nat. Bur. Stand. (U.S.) 72C (1968).

[7] Handbook of Chemistry and Physics , F9 (52nd Edition),Chemical Rubber Publishing Company, Cleveland, OH (1971).

[8] Precision Measurement and Calibration , U.S. Nat. Bur. Stand.

(U.S.) Handb. No. 77, Vol. Ill, Government Printing Office,

Washington, DC (1961) .

[9] R. M. Schoonover, J. Res. Nat. Bur. Stand. (U.S.) 8^, 341

(1980)

.

[10] B. E. Welch and V. E. Bean, Rev. Sci. Instrum. 5^, 1901

(1984) .

[II] D. P. Johnson, J. L. Cross, J. D. Hill and A. H. Bowman,

Industr. Engng. Chem. 49, 2046 (1957)

.

[12] B. E. Welch, R. E. Edsinger, V. E. Bean, and C. D. Ehrlich,

Observations of Gas Species and Mode of Operation Effects on

Effective Areas of Gas-Operated Piston Gages, in High PressureMetrology . G. F. Molinar, ed., Bureau International des Poids et

Mesures, Monographie 89/1, (1988), p. 81.

63

[13] J. C. Legras, V Bean, J. Jager, S. L. Lewis, G. F. Molinar,J. Phys. E. Sci. Instrum.

, 18, 361 (1985).

[14] W. Markus, Rev. Sci. Instrum. 41, 158 (1972).

[15] J. C. Houck, G. F. Molinar, and R. Maghenzani, J. Res. Nat.

Bur. Stand. (U.S.) 88 253 (1983).

[16] J. C. Lagras, S. L. Lewis, and G. F. Molinar, Metrologia,

25, 21, (1988)

.

[17] R. S. Dadson, in High Pressure Measurement Techniques ,

edited by G. N. Peggs (Applied Science Publishers, London, 1983),

pp. 39-43.

64

VI. APPENDIX: SAMPLE CALIBRATION REPORT

65

Nisr UNITED STATES DEPARTMENT OF COMMERCENational Institutse of Standards and TechnologyGaithersburg. Marvland 20893-0001

P-OOOOAThermophics Division

A- 55 Metrology Building

Requester

:

Any One Testing1234 Some Raod N. E.

Pick-a-City, Pick-a-State 12345-1234

Test Instrument Data:

Manufacturer: X Y Z Instrument CorporationModel: Pr 1111Serial Number: ZlllPiston Number: ZlllCylinder Number: ZC-ZOOOPressure Range: 1.38 MPa To 6.89 MPaCylinder Type: SimpleThermal Expansion Coefficient of Piston: 4.55xlO'V°CThermal Expansion Coefficient of Cylinder: 4.55xlO'V°CNominal Piston Area: 1.39x10"^ m^

Test Record Data:

Purchase Order Number and Date: TPO87654-43210 Dated 9/21/93NIST Identification Number: P-OOOOANIST Test folder Number: TN-912543-93Date Instrument was Received: November 31, 1993Date Test was Completed: December 31, 1993

Test Conditions:

NIST Standard and Calibration Reference: PG 42, August 1988Reference Temperature: 23°C

Pressure Fluid: Spinesso 22

Pressure Range of Calibration: 1.4 MPa To 6.9 MPaSurface Tension of Fluid: 3.09E-2Rotation of Weights: ManualTest Gage Weights Provided by: NISTThe test gage was leveled so that the axis of rotation was vertical.Reference level of test piston: The reference level is 0.073 meter belowthe uppermost surface of the piston. The gage was operated at mid-stroke.

The suggested fit for the effective area of the test gage is

Area = 1.422481x10"'' *[ 1 + (-1.481e-12 * P) ]

where P is the nominal pressure in Pa and the area is given in square jneters.

The total uncertainty is 66 ppm based on the approximate triple standard deviation.

The test gage was cross - floated against the NIST standard. The calibration data are givenin Table I. The pressures P are at the reference level of the test gage as determined by the

NIST standard gage. The temperature corrected forces F on the test gage were calculatedusing the expression

F =

1 + (ap + a,)(T - 23)

where are the masses of the piston, weight hanger and weights corresponding to P,

Pa is the density of the ambient air,

Pn, is the density of the material from which the weights are made,

g is the local acceleration due to gravity,

7 is the surface tension of the pressurizing fluid,

C is the circumference of the piston in the test gage,

ttp and Qc are the linear thermal expansivities of the piston and cylinder,and

,

T is the temperature in degrees C of the test gage when operating atpressure P.

Also listed in Table I is the area of the test gage at each pressure calculated using the

expression

A = F/P

To obtain an expression for calculating the area at any pressure, the P and A data have beenfitted to the following eight equations

F = [AJP (1)

F = [Ao]P t (2)

F = [Aod + bP)] (3)

F = [Aod + bP)]P - t (4)

F = [Aod + bP + cp2)]P (5)

F = [Aod + bP + cp2)]P - t (6)

F = [Aod + cp2) ]P (7)

F = [Aod + cp2)]P - t (8)

where the term in brackets is the area as a function of pressure, Ao is the extrapolated area

at zero applied pressure and at 23 °C, b and c are the first and second order pressure

coefficients for the area and t allows for the possibility of a tare. These coefficients and

the tripled standard deviation associated with each coefficient are listed in Table III.

-2-

The test gage was cross - floated against the NIST standard. The calibration data are givenin Table I. The pressures P are at the reference level of the test gage as determined by theNIST standard gage. The temperature corrected forces F on the test gage were calculatedusing the expression

F = ^i^i^^ - ^a/^m>S ^ 7C

1 + (ap + Q,)(T - 23)

where are the masses of the piston, weight hanger and weights corresponding to P,

Pa is the density of the ambient air,

is the density of the material from which the weights are made,

g is the local acceleration due to gravity,

7 is the surface tension of the pressurizing fluid,C is the circumference of the piston in the test gage,

Qp and are the linear thermal expansivities of the piston and cylinder,and

,

T is the temperature in degrees C of the test gage when operating atpressure P .

^

Also listed in Table I is the area of the test gage at each pressure calculated using the

expression

A = F/P

To obtain an expression for calculating the area at any pressure, the P and A data have beenfitted to the following eight equations

A = A„ (1)

A = A„ - t/P (2)

A = A,(l + bP) (3)

A = A„(l + bP) - t/P (4)

A = A„(l + bP + CP2) (5)

A = A,(l + bP + cp2) - t/P (6)

A = AJI + cp2) (7)

A = A„(l + cp2) - t/P (8)

where the term in brackets is the area as a function of pressure, A^ is the extrapolated area

at zero applied pressure and at 23 °C, b and c are the first and second order pressure

coefficients for the area and t allows for the possibility of a tare. These coefficients and

the tripled standard deviation associated with each coefficient are listed in Table III.

-2A-

P-8465TABLE I. CALIBRATION DATA

OBS. P F F/PNO. PRESSURE FORCE ON TEST GAGE EXP. AREA

(MPa) (N) (m^)

1.0 1.427626E+00 2.030777E+02 1.422485E-042.0 1.427626E+00 2.030777E+02 1.422485E-043.0 2.805465E+00 3.990692E+02 1.422471E-044.0 4.872209E+00 6.930563E+02 1.422468E-045.0 6.939003E+00 9.870519E+02 I.422469E-046.0 6.939003E+00 9.870519E+02 1.422469E-047.0 6.250043E+00 8.890501E+02 1.422470E-048.0 4.183310E+00 5.950625E+02 1.422468E-04y.O 4.183310E+00 5.950622E+02 1.422467E-04

10.0 2.116515E+00 3.010678E+02 1.422470E-049.0 7.629016E+01 1.281849E+03 1.680228E-05

10.0 3.493786E+01 5.870947E+02 1.680397E-05

TABLE II. COEFFICIENTS AND TRIPLED STANDARD DEVIATION OF THE COEFFICIENTSFROM FITS ACCORDING TO FORCE

FITNO. A„ ± AAq, b ± Ab, (Pa)"^ c ± Ac, (Pa)'^ t ± At, N

1 1.422470E-04 0 . OOOOOOE+00 O.OOOOOOE+00 O.OOOOOOE+002.415865E-10 O.OOOOOOE+00 0 . OOOOOOE+00 O.OOOOOOE+00

2 1.422466E-04 O.OOOOOOE+00 O.OOOOOOE+00 - 1 . 556432E-034.535476E-10 O.OOOOOOE+00 0 . OOOOOOE+00 2.081027E-03

3 1.422472E-04 -2 . 721360E-13 O.OOOOOOE+00 0 . OOOOOOE+001.007865E-09 1.192742E-12 O.OOOOOOE+OO O.OOOOOOE+00-

4 1.422447E-04 1.635692E-12 O.OOOOOOE+00 -4 . 680329E-03

1.397966E-09 1.152939E-12 O.OOOOOOE+OO 2.495582E-03

5 1.422488E-04 - 5 . 644814E- 12 5.434030E-19 O.OOOOOOE+OO

1.880300E-09 5.639562E-12 5.637140E-19 O.OOOOOOE+OO

6 1.422407E-04 9.370780E-12 - 6 . 158568E- 19 -8 . 718216E-03

5.103034E-09 9.613867E-12 7.621957E-19 5.352064E-03

7 1.422470E-04 O.OOOOOOE+OO -1 . 422632E-20 O.OOOOOOE+OO

6.618505E-10 O.OOOOOOE+OO 1.217329E-19 O.OOOOOOE+00

8 1.422456E-04 O.OOOOOOE+00 1.239066E-19 -3 . 716186E-03

8.983719E-10 O.OOOOOOE+00 1.011768E-19 2.190966E-03

P-8465TABLE III. COEFFICIENTS AND TRIPLED STANDARD DEVIATION OF THEC COEFFICIENTS

FROM FITS ACCORDING TO AREA

FITNO. Aq ± AA„, b ± Ab, (Pa)

-1c ± Ac, (Pa) t ± At, N

1.422472E-046.563554E-10

O.OOOOOOE+00O.OOOOOOE+00

O.OOOOOOE+00O.OOOOOOE+00

O.OOOOOOE+00O.OOOOOOE+00

1.422463E-046.179310E-10

O.OOOOOOE+00O.OOOOOOE+00

O.OOOOOOE+000 . OOOOOOE+00

2.819330E-031.566954E-03

1.422481E-041.192298E-09

1.481821E-121.826769E-12

O.OOOOOOE+00O.OOOOOOE+00

O.OOOOOOE+00O.OOOOOOE+00

1.42244IE-041.662107E-09

2.194630E-121.597867E-12

O.OOOOOOE+00O.OOOOOOE+00

5.631232E-032.238437E-03

1.422498E-041.612764E-09

8.910301E-126.351027E-12

8.864457E-197.450572E-19

O.OOOOOOE+00O.OOOOOOE+00

1.422401E-045.268654E-09

1.058918E-111.083068E-11

•7.183443E-199.206452E-19

9.268421E-034.978454E-03

1.422477E-049.297143E-10

O.OOOOOOE+00O.OOOOOOE+00

1.411765E-192.397935E-19

O.OOOOOOE+00O.OOOOOOE+00

1.422452E-041.049333E-09

O.OOOOOOE+00O.OOOOOOE+00

1.757731E-191.531932E-19

4.561128E-031.829370E-03

-4-

P-OOOOA

The suggested fit based on the calibration data is fit 3, yieldingfor the effective area

Area = [l+(bi P)

]

where P is the nominal pressure in Pa and the area is in square meters,chosen from the area fit.

The random uncertainty due to the calibration process can be expressed as

the tripled approximate standard deviation of the predicted values of thearea is 6.4 ppm. A measure of the total uncertainty of the area is thenobtained by adding this value to the three sigma estimated systematicuncertainty of the NIST standard used which is 60 ppm. Thus, the totaluncertainty of the effective area is 66 ppm. Note that this uncertainty is

applicable only over the stated range of calibration, and furthermore is validonly for the specific operating conditions of this calibration, given on page 1.

NOTE: The mass used for the piston assembly was .0838687 kg, based on a

density of 15.40 g/cm^ , as reported by X Y Z Instrument Corp.

For the Director,National Institute of Standardsand Technology

Charles D. Ehrlich, PhysicistGroup Leader, Pressure GroupThermophysics DivisionCenter for Chemical Technology

-5-

CE/DW/VBPOOOOATN 912543838/8384607

U.S. DEPARTMENT OF COMMERCENATIONAL INSTITUTE OF STANDARDS & TECHNOLOGY

CHEMICAL SCIENCE & TECHNOLOGY LABORATORYGAITHERSBURG, MD 2 0899

Calibration Report Appendix

ONE DOUBLE RANGE DEAD WEIGHT PISTON GAGESUBMITTED BY

ANYONE TESTING12 3 4 SOME ROAD N. E.PICK-A-CITY, PICK-A-STATE 12345-1234

INSTRUMENT RECEIVED: NOVEMBER 31, 1993 TEST COMPLETED: DECEMBER 31, 1993REFERENCE: THE PURCHASE ORDER NO.

TPO87654-43210 DATED SEPTEMBER 21, 1993

NIST IDENTIFICATION NO.: P1234MANUFACTURER: X Y Z INSTRUMENT CORPORATIONMANUFACTURER'S SERIAL NO.: ZlllMANUFACTURER'S TYPE NO.: 2345-432WEIGHTS WERE NOT RECEIVED WITH THE INSTRUMENT.

NOMINAL SIZE: 1.4E-4 SQ. METER

REFERENCE TEMPERATURE: T(S) = 23.0 °C.

The instrument was leveled so that the axis of rotation of the piston wasvertical

.

Observations were made with manual rotation of the weights on the test gage

The temperature was maintained near 23 °C and corrections were based onreadings of an attached thermometer.

NIST weights Were used in the calibration.

Reference level and piston position: The reference level is0.073 meter below the uppermost surface of the weight loadingtable. The gage was operated with the piston at mid-stroke.

The instrument was calibrated with Spinesstic No. 22 oilused as the pressure transmitting fluid.

If a tare error is indicated, it should be added algebraically,in Pa, to the pressure developed by the gage.

DESCRIPTION

PISTON NO. : ZlllCYLINDER NO.: ZC-ZOOO

PRESSURE RANGE: 1.3 8 MPA TO 6.89 MPACYLINDER TYPE: SIMPLE

Page 2

Values of characteristic parameters of the instrument are given inthe following table(s).

To facilitate the detection of errors the weight numbers, gagetemperatures, direction of rotation (l.=CW, -l.=^CCW) and jacketpressure Pj are listed for all observations. Observation numbers101 to 199 refer to the standard and 201 to 299 refer to the testinstrument. Mass and density of the weights are listed in thePROGRAM weight table on pages 3 and 3(a).

(S . NO

.

TEMP "C ROT p. (Pa)J

^ 'WEIGHT NUMBERS

101. 22 . 34 1. 0. 600 . 601

.

602 .

102 . 22 . 34 ' 1. 0. 600. 601. 602 .

103 . 22 . 37 1

.

0. 600 . 601. 602 . 92 .

104 . 22 . 39 1. 0. 600. 601. 602 . 92 . 93 .

105.105. 22 .41 1

.

0. 600 . 601

.

602 . 9 2 . 93 .

94 . 95.106. 22.41 1. 0. 600. 601

.

602 . 92 . 93 .

94 . 95 .

107 . 22.43 -1. 0. 600. 601

.

602 . 9 2 . 93 .

94 . 105 .

108 . 22 . 39 -1. 0. 600. 601. 602 . 92 . 93 .

109. 22 . 39 -1

.

0. 600. 601. 602 . 9 2 . 93 .

110. 22 .40 -1. 0. 600 . 601

.

602 . 105 .

201. 22 . 50 1. 0. 603 . 604 . 6 0 5. 606 . 607 .

608 . 609 . 6 3 0. 632 .

464 . 469 . 4 71. 4 / D .

202 . 22 . 50 -1

.

0. 603 . 604 .^ r\ r' 607 .

608 . 609 .c ^ r\b J U . 632 .

464 . 469 . 4 / 1 . 4 / o •

203 . 22.51 1. 0. 603 . 604 .r\ r\ rO (J b . 607 .

608 . 609 . 610. 611. 612 .

613 . 627 . 6 3 0. 4 64. 469 .

473 . 474 . 475 . 4 7 6. 632 .

204 . 22 . 51 -1. 0. 603 . 604 . 605. 606. 607 .

608 . 609 . 610 . 611. 612 .

613 . 614 » 615 . 616. 617 .

618 . 619 . 627 . 630 . 464 .

470. 474 . 477 . 632 .

205. 22.51 1. 0. 603 . 604 . 605 . 606 . 607 .

608 . 609 . 610 . 611. 612 .

613 . 614 . 615 . 616 . 617 .

618 . 619 . 620. 621. 622 .

623 . 624 . 625 . 627 . 630.632 . 464 . 470 . 473 . 477 .

206. 22 . 51 -1. 0. 603 . 604 . 605 . 606 . 607 .

608 . 609 . 610. 611. 612 .

613 . 614 . 615 . 616. 617 .

618 . 619 . 620 . 621. 622 .

623 . 624 . 625 . 627 . 630 .

632 . 464 . 470. 473 . 477 .

PAGE 2 [cont'd]

2 07 . 22.53 1

.

0 . 603 . 604 . 605. 606. 607 .

608 . 609 . 610. 611. 612 .

613 . 614 . 615 . 616 . 617 .

618 . 619 . 620. 621. 622 .

626. 627 . 628 . 631. 632 .

461. 466 . 468 . 470 . 472 .

2 08 . • 22.48 1. 0. 603 . 604 . 605. 606 . 607 .

608 . 609 . 610. 611. 612 .

613 . 614 . 615 . 616 . 617 .

627 . 630. 632 . 464 . 469.476.

209. 22.48 -1. 0. 603 . 604 . 605 . 606. 607 .

608 . 609 . 610. 611

.

612 .

613 . 614 . 615. 616 . 617 .

627 . 630 . 632 . 464 . 469 .

477 .

210. 22.48 -1. 0. 603 . 604 . 605. 606 . 607 .

608 . 609 . 610. 611

.

627 .

630. 632 . 464 . 469 . 476.

Page 3

Weights not listed in the Program Weight Table are assigned numbers600 to 699. Those used in this run ARE listed on this page. Theyinclude piston, weight hangers etc. of the instrument under test.

DENSIT^(g/cm )

600

.

0 . 083868700 15 . 400601

.

0 . 344963100.J T T \J ~J _i. \J \J 7 . 800602 . 11

.

799716000 7 . 800603 . 0 . 081155840 8 . 400604 . 0 . 1 74999565 8 . 400605

.

1

.

013779200 7 . 800606 . 0 . 804402000 7 .800607 4 , 999401 500 7 .800\J \J •

R• 00024 5000 7 .800

609 . 5 . 00028 ] 000 7 . 800610 . 5 . 000102000\J \J \J ^ \J \j \J \J 7 . 800611

.

5 . 000275000 7 . 800612 . 4 . 999945000 7 . 800613 . 5 . 000188000\J \J \J -1- W \J \J \J 7 . 800614 . 5 . 00003 5000 7 . 800615 . 5 . 000232000\J V-* \J £-1 €-1 \J \J \J 7 . 800616 . 5 . 000163000 7 . 800617 . 5 . 000203000 7 . 800618 . 5 . 000297000 7 . 800619 . 5 . 000316000 7 .800620 . 5 . 000114 000 7 .8006? 1 4 qqqqQnOOO 7 . 800622 . 5. 000261000 7 .800623 . 5. 000019000 7 .800624 . 5 . 000220000 7 .800625. 5. 000194000 7 .800626. 3 . 000027000 7 .800627 . 3 . 000075000 7 .800628 . 2 . 000027000 7 .800629 . 0. 999983000 7 .800630. 0 . 500019700 7 .800631. 0. 300001000 7 .800632 . 0. 099997800 8 .400

Page 3 [cont'd]

Listed are the characteristics of the standard used in this testand available data for the instrument under test.

CHARACTERISTICS OF THE STANDARD

1 . 4200000E+028 . 4021380E-05•2 . 4000000E-120 . OOOOOOOE+000 , OOOOOOOE+003 . 2480000E-020 . OOOOOOOE+004 . llOOOOOE-064 . llOOOOOE-060 . OOOOOOOE+002 . 3000000E+010 . OOOOOOOE+000 . OOOOOOOE+000 . OOOOOOOE+000 . OOOOOOOE+000 . OOOOOOOE+000 . OOOOOOOE+000 . OOOOOOOE+008 . 6000000E-052 . 4000000E-120 . OOOOOOOE+00

Standard^

Area in mPressure Coefficient '1 in PaPressure Coefficient in Pa

Circumference of Piston ip mOil Buoyancy (volume in m ) Correction Above CylinderThermal Expansivity of Piston °C

^

Thermal Expansivity of Cylinder °C

Reference Temperature of Standard °C(Pa)

S^ (Pa'N'^)

Qz (Pa N"^)

D (Pa')

E (Pa N)

F (Pa N )

3 Sigma A/A

Zero Clearance Jacket Pressure (Coeff)

Jacket Pressure Distortion (Coeff)

Sigma b^

Sigma b-

CHARACTERISTICS OF INSTRUMENT UNDER TEST

2 . OOOOOOOE+021 . 4200000E-040 . OOOOOOOE+000 . OOOOOOOE+000 . OOOOOOOE+004 . 2400000E-020 . OOOOOOOE+004 . 5500000E-064 . 5500000E-061 . 6300000E-012 . 3000000E+018 . 5780000E-010 . OOOOOOOE+003 . 0930000E-02

Instrumen|: Under TestArea in mPressure Coefficient b From Previous Calibration in Pa

-1

-1

Circumference of Piston ip mOil Buoyancy (volume in m )

Thermal Expansivity of Piston °CThermal Expansivity of Cylinder °CDifference in Reference Levels in mReference Temperature of the Insti^ument Under TestDensity of Pressure Fluid in g/cm

^

Pressure Coefficient of Density in Pa^

Surface Tension of Pressure Fluid in N m

Page 3(a)

Masses listed in the Program Weight Table are assignednumbers 001 to 599, and 701 to 2000.

Those used in this calibration are listed on this page.

* File 6tab81.tab MASS TABLE VALUES AS OF 09/91

Air Density used 0.00118 q/cia Local Gravity is 9.801010 m/s^

NUMBER MASS DENSITYkg g/cm

92 . . 118133230E+02 0. 840E+0193 . . 118132960E+02 0 . 840E+0194 . . 118130970E+02 0. 840E+0195. . 118132870E+02 0. 840E+01

105. . 590641670E+01 0. 840E+01461. . 226798910E+00 0. 780E+01464 . . 453600990E-01 0. 780E+01466. . 136078170E-01 0. 780E+01468 . . 453596910E-02 0. 780E+01469. . 226802130E-02 0. 780E+01470. . 136066550E-02 0. 780E+01471. . 907253680E-03 0. 780E+01472 . . 453621850E-03 0. 166E+02473 . . 226796410E-03 0. 166E+02474 . . 136055750E-03 0. 166E+02475. . 907930890E-04 0. 166E+02476. . 454732690E-04 0. 166E+02477 . .227166310E-04 0. 270E+01

Page 4

This table lists the force generated by the load on the standardinstrument. An air buoyancy correction has been applied. Also listedare the corrections for surface tension, temperature, jacket pressureand pressure coefficient of the standard.

FORCE SURFACE TEMPERATURE JACKET PRESS. FRACTIONALNO. STD (N) TENS. (N) CORR . STD PRESSURE COEFF. CHANGE (d)

101. 1.19834E+02102. 1.19834E+02103. 2.35600E+02104. 4.09247E+02105. 5.82896E+02106. 5.82896E+02107. 5.25011E+02108. 3.51366E+02109. 3.51366E+02110. 1.77715E+02

1 . 00461E-031 . 00461E-031 . 00461E-031 . 00461E-031 . 00461E-031. 00461E-031. 00461E-031 . 00461E-031 . 00461E-031 . 00461E-03

9 . 99995E-019 . 99995E-019 . 99995E-019 . 99995E-019 . 99995E-019 . 99995E-019 . 99995E-019 . 99995E-019 . 99995E-019 . 99995E-01

l.OOOOOE+00 9

l.OOOOOE+00 9

l.OOOOOE+00 9

l.OOOOOE+00 9

l.OOOOOE+00 9

l.OOOOOE+00 9

l.OOOOOE+00 9

l.OOOOOE+00 9

l.OOOOOE+00 9

l.OOOOOE+00 9

99997E-0199997E-0199993E-0199988E-0199983E-0199983E-0199985E-0199990E-0199990E-0199995E-01

0 . OOOOOE+000 . OOOOOE+000 . OOOOOE+000 . OOOOOE+000 . OOOOOE+000 . OOOOOE+000 . OOOOOE+000 . OOOOOE+000 . OOOOOE+000 . OOOOOE+00

Page 5

This table lists the force generated by the load on the instrumentunder test. An air buoyancy correction has been applied. Also listedare the corrections for surface tension, temperature and fluid headin the connecting lines between the two instruments.

FORCE FLUID BUOY. SURFACE TEMP. CORR. HEAD CORR.NO. TEST (N) TEST (N) TENS. (N) TEST (Pa)

201. 0. 2030754E+03 0 . OOOOOOOE+00 0. 1311432E- 02 0 . 9999955E+00 -0 ^1368504E+04202 . 0. 2030754E+03 0 . OOOOOOOE+00 0. 1311432E- 02 0 . 9999955E+00 -0 . 1368504E+04203 . 0. 3990661E+03 0 . OOOOOOOE+00 0. 1311432E- 02 0 . 9999955E+00 -0 . 1368504E+04204 . 0. 6930518E+03 0 . OOOOOOOE+00 0 . 1311432E- 02 0 . 9999955E+00 -0 . 1368504E+04205. 0. 9870462E+03 0 . OOOOOOOE+00 0 . 1311432E- 02 0 . 9999955E+00 -0 . 1368504E+04206. 0 . 9870462E+03 0 . OOOOOOOE+00 0. 1311432E- 02 0 . 9999955E+00 -0 . 1368504E+04207 . 0. 8890450E+03 0 . OOOOOOOE+00 0. 1311432E- 02 0 . 9999957E+00 -0 . 1368504E+04208 . 0. 5950584E+03 0 . OOOOOOOE+00 0. 1311432E- 02 0 . 9999953E+00 -0 . 1368504E+04209. 0. 5950581E+03 0 . OOOOOOOE+00 0. 1311432E- 02 0 . 9999953E+00 -0 . 1368504E+04210. 0. 3010651E+03 0 . OOOOOOOE+00 0. 1311432E- 02 0 . 9999953E+00 -0 . 1368504E+04

Page 6

After computation of the pressure generated by the standard at thereference level of the instrument under test, the following functionsare fitted to the data.

FORCE EQUATIONS

FIT 1 F=PAqFIT 2 F=PAq - tFIT 3 F=PAq [ 1+ (b^ P) ]

FIT 4 F=PAq [l+(b^ P) ]

FIT 5 F=PAo [l+(bi P) + (b2 P) ]

FIT 6 F=PAq [l+(bi P) + (b2 P) ]

FIT 7 F=PAq [l+(b2 P) ]

FIT 8 F=PAq [l+(b2 P ) ] - t

- t

With: F Force on test instrumentP Pressure at Ref Level^0 Effective Area of test instrument at Zero pressureb^ and b2 Pressure Coefficientst Tare Weight (force)

.

This table lists the observation numbers, pressure and the residualsof the fits converted to the equivalent pressures.

OBS.NO.

PRESSUREkPa

RESIDUALSFIT l,Pa

RESIDUALSFIT 2, Pa

RESIDUALSFIT 3, Pa

RESIDUALSFIT 4, Pa

0 0. OOOOOOE+00 0. OOOOOE+00 - 0. 10942E+02 0. OOOOOE+00 -0. 32903E+021 0. 142763E+04 0 . 15982E+02 0 . 80931E+01 0. 14300E+02 0. 23669E+012 0. 142763E+04 0 . 15982E+02 0. 80931E+01 0. 14300E+02 0. 23669E+01.0 0 . 211651E+04 -0 . 61656E-01 - 0. 64775E+01 •-0. 21580E+01 -0. 67546E+013 0. 280547E+04 0 . 21611E+01 - 0 . 27815E+01 -0. 91617E-01 0. 83833E+008 0 . 418331E+04 -0 . 44270E+01 - 0 . 64232E+01 •-0. 62175E+01 0 . 33221E+009 0 . 418331E+04 -0 . 59954E+01 - 0 . 79916E+01 -0. 77859E+01 -0. 12362E+014 0. 487221E+04 -0. 47538E+01 - 0. 52769E+01 •-0. 59258E+01 0. 71743E+007 0. 625004E+04 0. 36083E+01 0. 60315E+01 0. 44484E+01 0 . 58459E+015 0. 693900E+04 -0. 53004E+00 0. 33665E+01 0. 17036E+01 -0. 22384E+016 0. 693900E+04 -0. 53004E+00 0. 33665E+01 0. 17036E+01 -0. 22384E+01

)BS. PRESSURE RESIDUALS RESIDUALS RESIDUALS RESIDUALSNO. kPa FIT 5, Pa FIT 6, Pa FIT 7, Pa FIT 8, Pa

0. 0 . OOOOOOE+00 0 . OOOOOOE+00-0 . 612893E+02 0. OOOOOOE+00 -0. 261249E+021. 0 . 142763E+04 0 . 689423E+01 0. 464599E+00 0. 153068E+02 0. 302773E+012 . 0 . 142763E+04 0. 689423E+01 0. 464599E+00 0. 153068E+02 0. 302773E+01

10. 0 . 211651E+04 -0 . 811235E+01-•0. 397241E+01 -0. 989297E+00 -0 . 730094E+013 . 0 . 280547E+04 -0 . 276921E+01 0. 467506E+01 0. 106687E+01 -0. 109428E+008 . 0 . 418331E+04 -0 . 113204E+01 0. 219682E+00 -0. 548556E+01 0. 267605E-019. 0 . 418331E+04 -0. 270047E+01-•0. 134875E+01 -0. 705400E+01 -0. 154167E+014 . 0 . 487221E+04 0. 151389E+01-0. 198239E+01 -0. 555432E+01 0. 969509E+007 . 0 . 625004E+04 0. 821196E+01 0. 278647E+01 0. 394397E+01 0. 647049E+015. 0 . 693900E+04 -0. 269595E+01-•0. 653431E+00 0. 739648E+00 -0. 228509E+016. 0 . 693900E+04 -0. 269595E+01-•0. 653431E+00 0. 739648E+00 -0. 228509E+01

PAGE 6A

This table lists the observation numbers, pressure and the standarddeviations of the predicted values, expressed in Parts Per Million(ppm)

.

)BS. PRESSURE 3 SD PRED 3 SD PRED 3 SD PRED 3 SD PREDNO. KPA FIT l,ppm FIT 2, ppm FIT 3, ppm FIT 4, ppm

0. 0. OOOOOOE+00 0. OOOOOOE+00 0. 693676E-03 0. OOOOOOE+00 0 . 831861E-031. 0. 142763E+04 0. 169834E+01 0 . 752192E+01 0. 545154E+01 0. 510055E+012 . 0. 142763E+04 0. 169834E+01 0. 752192E+01 0 . 545154E+01 0 . 510055E+01

10. 0. 211651E+04 0 . 169836E4-01 0. 429170E+01 0 . 468090E+01 0 . 242395E+013 . 0. 280547E+04 0 . 169836E+01 0 . 274598E+01 0 . 393084E+01 0. 179695E+018 . 0. 418331E+04 0 . 169836E+01 0 . 154878E+01 0 . 256607E+01 0 . 143516E+019. 0. 418331E+04 0 . 169836E+01 0 . 154878E+01 0 . 256608E+01 0 . 143516E+014 . 0 . 487221E+04 0 . 169836E+01 0 . 141854E+01 0 . 204377E+01 0 . 118026E+017 . 0. 625004E+04 0 . 169836E+01 0. 150345E+01 0 . 184729E+01 0 . 848793E+005. 0. 693900E+04 0 . 169836E+01 0 . 159854E+01 0. 224855E+01 0 . 106683E+016. 0. 693900E+04 0. 169836E+01 0. 159854E+01 0. 224855E+01 0. 106683E+01

)BS. PRESSURE 3 SD PRED 3 SD PRED 3 SD PRED 3 SD PREDNO. KPA FIT 5, ppm FIT 6, ppm FIT 7, ppm FIT 8, ppm

0. 0. OOOOOOE+00 0. OOOOOOE+00 0 . 178402E-02 0. OOOOOOE+00 0 . 730322E-031. 0. 142763E+04 0 . 666613E+01 0 . 424899E+01 0 . 442474E+01 0 . 552048E+012 . 0. 142763E+04 0 . 666613E+01 0 . 424899E+01 0 . 442474E+01 0 . 552048E+01

10. 0. 211651E+04 0. 446395E+01 0 . 247184E+01 0. 415465E+01 0. 269989E+013 . 0. 280547E+04 0 . 300438E+01 0 . 218358E+01 0. 378619E+01 0. 188354E+018 . 0. 418331E+04 0. 224036E+01 0. 110234E+01 0 . 280796E+01 0 . 158784E+019. 0. 418331E+04 0. 224036E+01 0. 110234E+01 0 . 280796E+01 0. 158784E+014 . 0. 487221E+04 0. 216431E+01 0. 113640E+01 0 . 227432E+01 0 . 137160E+017 . 0. 625004E+04 0. 147214E+01 0. 889763E+00 0. 184583E+01 0, 940994E+005. 0. 693900E+04 0. 175083E+01 0. 866464E+00 0. 237642E+01 0 . 119983E+016. 0. 693900E+04 0. 175083E+01 0. 866464E+00 0. 237642E+01 0 . 119983E+01

I

I

Page 7

In order to detect any effect due to the rotational direction of the '

pistons, the residuals from FIT 6 are separated with respect to thedirection of rotation of the pistons and tabulated.

)BS . PRESSURE 1=CW TEST TEST 1=CW STD. STD.NO. kPa 1=CCW CW, Pa CCW,Pa -1=CCW CW, Pa CCW,Pa

0. 0 . OOOOE+00 0. 0. OOOOE+00 0 . OOOOE+00 0. 0 . OOOOE+00 0. OOOOE+001. 0 . 1428E+ 04 1. 0. 4646E+00 0 . OOOOE+00 1. 0 . 4646E+00 0. OOOOE+002 . 0 . 1428E+04 -1. 0 . OOOOE+00 0 . 4646E+00 1. 0. 4646E+00 0. OOOOE+00

10. 0 . 2117E+04 -1. 0. OOOOE+00 3972E+01 -1. 0. OOOOE+00 3972E+013 . 0 . 2805E+04 1

.

0 . 4675E+01 0. OOOOE+00 1. 0. 4675E+01 0 . OOOOE+008 . 0 . 4183E+04 1. 0. 2197E+00 0. OOOOE+00 -1. 0. OOOOE+00 0. 2197E+009 . 0 . 4183E+04 -1. 0. OOOOE+00 1349E+01 -1. 0. OOOOE+00 1349E+014 . 0 . 4872E+04 -1. 0. OOOOE+00 1982E+01 1. 1982E+01 0. OOOOE+007 . 0 . 6250E+04 1. 0. 2786E+01 0. OOOOE+00 -1. 0. OOOOE+00 0. 2786E+015. 0 . 6939E+04 1

.

6534E+00 0. OOOOE+00 1. 6534E+00 0. OOOOE+006. 0 . 6939E+ 04 -1

.

0 . OOOOE+00 6534E+00 1. 6534E+00 0. OOOOE+00

PAGE 8

The results of the test, as determined by using the FORCE EQUATIONS,are compiled in this table. It lists the coefficients and theirtripled standard deviations due to random sources of error and, forthe highest pressure, the uncertainty in pressure due to theuncertainty in these coefficients.

COEFF, FIT 1 COEFF, FIT 2 COEFF, FIT 3 COEFF, FIT 4

1.422470E-040 . OOOOOOE+000 . OOOOOOE+000 . OOOOOOE+00

1. 422466E-040 . OOOOOOE+000 . OOOOOOE+000 . OOOOOOE+00

1. 422472E-042 . 721360E-130. OOOOOOE+000 . OOOOOOE+00

422447E-04 AREA, M635692E-12 PRES COEF b

0 . OOOOOOE+000. OOOOOOE+00 -1. 556432E-03 0. OOOOOOE+00 -4 . 68 0 3 2 9E-0 3 TARE, N

Pa-1

OOOOOOE+00 PRES COEF b^ Pa

1. 698359E-06 3 . 188460E-06 7 . 085308E-06 9 . 827898E-06 3 STD DEV0 . OOOOOOE+00 0. OOOOOOE+00 1. 192742E-12 1. 152939E-12 3 STD DEV0. OOOOOOE+00 0. OOOOOOE+00 0. OOOOOOE+00 0. OOOOOOE+00 3 STD DEV0. OOOOOOE+00 0. OOOOOOE+00 0. OOOOOOE+00 0. OOOOOOE+000 . OOOOOOE+00 2 . 081027E-03 0. OOOOOOE+00 2 . 495582E-03 3 STD DEV

2.464246E-02 2.047674E-02 2.540394E-02 1.155705E-02 3 RES STD DEV kPaAP

1.698359E-06 5.296785E-06 1.536175E-05 2.035646E-05 3 STD DEV A, /A„ ate ' e

COEFF, FIT 5 COEFF, FIT 6 COEFF, FIT 7 COEFF, FIT 8

1.422488E-04 1

•5. 644814E-12 9

5.434030E-19 -6

422407E-04 1

370780E-12 0

158568E-19 -1

422470E-04OOOOOOE+00422632E-20

1.422456E-04 AREA, M0. OOOOOOE+00 PRES COEF b

0. OOOOOOE+00 0. OOOOOOE+00 0. OOOOOOE+00 0. OOOOOOE+000. OOOOOOE+00 -8 . 718216E-03 0. OOOOOOE+00 -3 . 7 1 6 18 6E-0 3 TARE, N

Pa-1

1.239066E-19 PRES COEF b. Pa

1. 321839E-055. 639562E-125. 637140E-190. OOOOOOE+000. OOOOOOE+00

3 . 587605E-059 . 613867E-127 . 621957E-190. OOOOOOE+005. 352064E-03

4 . 652826E-060. OOOOOOE+001. 217329E-190. OOOOOOE+000. OOOOOOE+00

6. 315639E-060. OOOOOOE+001. 011768E-190 . OOOOOOE+002 . 190966E-03

STD DEV Aq /aSTD DEV b

0 -1

1

STD DEV Pa"^

3 STD DEV T, N

1.833163E-02 8.873121E-03 2.593875E-02 1.279243E-02 3 RES STD DEV kPa7.949402E-05 1.447085E-04 1.051424E-05 1.340698E-05 3 STD DEV A^ /A^ at

P

\

P(Pa)

0. 14276260E+070. 14276260E+070 . 28054650E+070. 48722090E+070. 69390030E+070 . 69390030E+070. 62500430E+070. 41833100E+070 . 41833100E+070 . 21165150E+07

PAGE

AREA

,

0. 14224854E-030 . 14224854E-030 . 14224708E-030. 14224684E-030. 14224694E-030. 14224694E-030 . 14224704E-030. 14224681E-030. 14224674E-030. 14224696E-03

P(MPa)

0. 14276260E+010 . 14276260E+010 . 28054650E+010 . 48722090E+010. 69390030E+010 . 69390030E+010 . 62500430E+010. 41833100E+010. 41833100E+010. 21165150E+01

2AREA , mm

0. 14224854E+030 . 14224854E+030. 14224708E+030. 14224684E+030. 14224694E+030. 14224694E+030. 14224704E+030. 14224681E+030. 14224674E+030. 14224696E+03

This data represents the effective area of theTEST GAGE, determined as the full air buoyancy correctedforce on the test gage divided by the pressure at thereference level of the test gage. The equations on PAGE 10are fit to this data.

Area vs Pressure [Data on Page 9)

1.42250E+02 ,

1.42249E+02

E

u(0

w

L

<

1.42249E+02

I.42248E+02 -

1.4224aE+02

1.42247E+02

1.42247E+02

1,42246E+02

1 2 3 4 5 6 ?

Pressure (MPa)

PAGE 10

After computation of the pressure generated by the standard at thereference level of the instrument under test the following functionsare fitted to the data.

AREA EQUATIONS

FIT 1 A-AqFIT 2 A=An - (t/P)FIT 3 A=Aq [ 1+ (b^ P) ]

FIT 4 A-Aq [l+(b^ P) ] - (t/P)

FIT 5 A-Aq [l+(bi P) + (b2 PJ ]

FIT 6 A=Ao [l+(bi P) + (b2 P ) ] - (t/P)FIT 7 A=Ao [l+(b2 P

)

]

FIT 8 A=Aq [l+(b2P)] - (t/P)

With: P Pressure at Ref LevelA Effective Area of Test Instrument at each observationb^ and b2 Pressure Coefficientst Tare (force in newtons)

This table lists the observation numbers, pressure and the residualsof the fits converted to the equivalent pressures.

OBS

.

NO.PRESSURE

kPaRESIDUALSFIT l,Pa

RESIDUALSFIT 2, Pa

RESIDUALSFIT 3, Pa

RESIDUALSFIT 4, Pa

1. 0 . 142763E+04 0. 130298E+02 0 . 272127E+01 0 . 734600E+01 0. 857584E+002 . 0 . 142763E+04 0. 130298E+02 0 . 272127E+01 0. 734600E+01 0. 857584E+003 . 0. 280547E+04 -0. 324452E+01 -0 . 437363E+01 -0. 868611E+01 0. 255919E+014 . 0 . 487221E+04 -0. 138593E+02 -0 . 121910E+01 -0 . 838813E+01 0. 328502E+015 . 0 . 693900E+04 -0. 147186E+02 0 . 116912E+02 0 . 143251E+02 -0. 498220E+016 . 0. 693900E+04 -0 . 147186E+02 0 . 116912E+02 0. 143251E+02 -0. 498220E+017 . 0 . 625004E+04 -0 . 880864E+01 0 . 130111E+02 0. 109705E+02 0. 548043E+018 . 0 . 418331E+04 -0. 127313E+02 -0. 468078E+01 -0. 123042E+02 0. 271600E+019 . 0 . 418331E+04 -0. 148403E+02 -0. 678980E+01 -0. 144132E+02 0 . 606976E+00

10 . 0 . 211651E+04 -0. 425524E+01 -0 . 997434E+01 -0 . 105213E+02 -0. 639840E+01

)BS. PRESSURE RESIDUALS RESIDUALS RESIDUALS RESIDUALSNO. kPa FIT 5, Pa FIT 6, Pa FIT 7, Pa FIT 8, Pa

1. 0 . 142763E+04 0 . 291558E+01 0 . 256754E+00 0. 919752E+01 0. 112396E+012 . 0. 142763E+04 0 . 291558E+01 0. 256754E+00 0. 919752E+01 0. 112396E+013 . 0 . 280547E+04 -0 . 318241E+01 0. 536278E+01 -0. 846554E+01 0. 142916E+014 . 0. 487221E+04 0. 744012E+01 -0 . 200112E+01 -0 . 120120E+02 0. 429009E+015. 0 . 693900E+04 -0 . 675284E+01 -0. 373053E+00 0. 118264E+02 -0. 504226E+016. 0 . 693900E+04 -0 . 675284E+01 -0. 373053E+00 0. 118264E+02 -0. 504226E+017 . 0 . 625004E+04 0 . 103418E+02 0 . 244383E+01 0 . 708297E+01 0. 670576E+018 . 0. 418331E+04 0. 301154E4-01 0. 698928E-02 -0. 148295E+02 0. 290519E+019 . 0. 418331E+04 0. 902523E+00 -0. 2102C3E+01 -0. 169385E+02 0. 796166E+00

10. 0. 211651E+04 -0 . 108392E+02 -0 . 347787E+01 -0. 920735E+01 -0. 734207E+01

PAGE lOA

This table lists the observation numbers, pressure and the standarddeviations of the predicted values, expressed in Parts Per Million(ppm)

.

BS . PRESSURE 3 SD PRED 3 SD PRED 3 SD PRED 3 SD PREDNO. KPA FIT l,ppin FIT 2, ppm FIT 3, ppm FIT 4, ppm

1

.

0. 142763E+04 0 . 461415E+01 0. 461149E+01 0 . 615248E+01 0 . 282817E4-012 . 0. 142763E+04 0. 461415E+01 0. 461149E+01 0 . 615248E+01 0 . 282817E+013 . 0. 280547E+04 0 . 461419E+01 0 . 228254E+01 0. 441376E+01 0. 223057E+014 . 0. 487221E+04 0 . 461420E+01 0 . 269055E+01 0. 395981E+01 0 . 169360E+015 . 0. 693900E+04 0. 461420E+01 0 . 310396E+01 0 . 635519E+01 0 . 250502E+016 . 0. 693900E+04 0 . 461420E+01 0 . 310396E+01 0 . 635519E+01 0. 250502E+017 . 0 . 625004E+04 0. 461419E+01 0. 298745E+01 0 . 538369E+01 0. 193579E+018 . 0. 418331E+04 0 . 461420E+01 0. 251077E+01 0 . 371208E+01 0 . 193922E+G19 . 0. 418331E+04 0 . 461420E+01 0. 251077E+01 0. 371208E+01 0. 193922E+01

10 . 0 . 211651E+04 0. 461420E+01 0. 272312E+01 0 . 520424E+01 0 . 199682E+01

)BS . PRESSURE 3 SD PRED 3 SD PRED 3 SD PRED 3 SD PREDNO. KPA FIT 5, ppm FIT 6, ppm FIT 7, ppm FIT 8, ppm

1. 0. 142763E+04 0 . 470577E+01 0. 227341E+01 0 . 616617E+01 0 . 315861E+012 . 0. 142763E+04 0 . 470577E+01 0 . 227341E+01 0. 616617E+01 0 . 315861E+013 . 0. 280547E+04 0. 325791E+01 0. 216203E+01 0 . 521770E+01 0 . 233687E+014 . 0. 487221E+04 0. 371623E+01 0. 191900E+01 0 . 420086E+01 0. 201089E+015. 0. 693900E+04 0. 478399E+01 0. 213336E+01 0 . 771056E+01 0. 291659E+016. 0. 693900E+04 0 . 478399E+01 0 . 213336E+01 0 . 771056E+01 0 . 291659E+017 . 0. 625004E+04 0 . 342834E+01 0 . 163487E+01 0 . 599034E+01 0 . 213567E+018 . 0. 418331E+04 0. 387989E+01 0 . 172684E+01 0 . 423772E+01 0. 227451E+019 . 0. 418331E+04 0. 387990E+01 0. 172684E+01 0 . 423772E+01 0 . 227451E+01

10. 0. 211651E+04 0. 331547E+01 0. 235774E+01 0. 574685E+01 0. 207900E+01

Res i dua Is of Fit 1

cd

Q.

(0

cn

-10 -

^ 5

Thousands

Pressure C PaD

Res i dua Is of Fit 2

da

(du

cr

^ 5

Thousands

Pressure CP^D

Res i dua Is of Fit 3

a

m

en

-20

Pressure (Pa^

Res i dua I s of Fit 4

cd

u"D

(D

cr

4 5

Thousands

Pressure C

Residuals of Fit 5

CO

"D

0]

(U

Thousands

Pressure CPaD

Res i dua I s of Fit 6

CO

aw

d

(U

Pressure CP^D

Residuals in ppm C3 Signna Error Bars Applied^ Fit 1

10I

Eaa

CO

<

(S)

(d

T3

m

4 5

Thousands

Pressure C^Ps.^

Residuals in ppm C3 Sigma Error Bars App I ( ed^ Fit 3

10I

12345678Thousands

Pressure C^Pa)

Residuals (n ppm C3 Sigma Error Bars Applied^ Fit 6

3I

II I I I I I

1 2345678Thousonds

Pressure C^Pa])

PAGE 2 3

The results of the test, as determined by using the AREA EQUATIONS,are compiled in this table. It lists the coefficients and theirtripled standard deviations due to random sources of errors and,for the highest pressure, the uncertainty in pressure due to theuncertainty in these coefficients.

COEFF, FIT 1 COEFF, FIT 2 COEFF, FIT 3 COEFF, FIT 4

1. 422472E-040. OOOOOOE+000 . OOOOOOE+000 . OOOOOOE+000 . OOOOOOE+00

1 . 422463E-040. OOOOOOE+000 . OOOOOOE+000 . OOOOOOE+00

-2 . 819330E-03

1. 422481E-04•1.481821E-120 . OOOOOOE+000 . OOOOOOE+000 . OOOOOOE+00

1.422441E-04 AREA, m2.194630E-12 PRES COEF0. OOOOOOE+00 PRES COEF0 . OOOOOOE+00

-5. 631232E-03 TARE, N

PaPa"

4 . 614187E-06 4 . 344092E-06 8 . 381819E-06 1

.

168489E-05 3 STD DEV0. OOOOOOE+00 0 . OOOOOOE+00 1. 826769E-12 1

.

597867E-12 3 STD DEV0. OOOOOOE+00 0 . OOOOOOE+00 0 . OOOOOOE+00 0. OOOOOOE+00 3 STD DEV0 . OOOOOOE+00 0 . OOOOOOE+00 0 . OOOOOOE+00 0 . OOOOOOE+000. OOOOOOE+00 1. 566954E-03 0. OOOOOOE+00 2 . 238437E-03 3 STD DEV T,

PaPa

1. 459134E-054 . 614187E-06

7 . 183315E-065 . 931598E-06

1. 173177E-052 . 105778E-05

4.149265E-06 3 RES STD DEV A/A2.504029E-05 3 STD DEV A„ /A„ at

e ' e

COEFF, FIT 5 COEFF, FIT 6 COEFF, FIT 7 COEFF, FIT 8

1. 422498E-048 . 910301E-128 . 864457E-190 . OOOOOOE+000 . OOOOOOE+00

1 . 422401E-041. 058918E-11•7 . 183443E-190 . OOOOOOE+00•9 . 268421E-03

1. 422477E-040 . OOOOOOE+001. 411765E-190 . OOOOOOE+000 . OOOOOOE+00

1.422452E-04 AREA, mO.OOOOOOE+00 PRES COEF1.757731E-19 PRES COEF0. OOOOOOE+00

-4 . 561128E-03 TARE, N

PaPa"

-1

1. 133755E-056. 351027E-127 . 450572E-190. OOOOOOE+000. OOOOOOE+00

3 . 704057E-051 . 083068E-119 . 206452E-190 . OOOOOOE+004 . 978454E-03

6. 535885E-060. OOOOOOE+002 . 397935E-190. OOOOOOE+000 . OOOOOOE+00

7 . 376934E-060 . OOOOOOE+001. 531932E-190. OOOOOOE+001. 829370E-03

STD DEV Aq /Aq^

STD DEV b^ PaSTD DEV b^ Pa

-2

3 STD DEV T, N

7.468447E-06 3.240224E-06 1.312718E-05 4.679866E-06 3 RES STD DEV A/A9.128167E-05 1.615673E-04 1.808189E-05 1.660652E-05 3 STD DEV A^ /A^ at

Run 01/04/94 11:09:22.45Pmax

As shown in the Residual Plots in ppm on the preceeding pages theMaximum uncertainty values in ppm for Fits 1-6 are:

1 2 3 4 5 6

9.1 4.7 6.4 3.0 5.1 2.4

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